Exhibit 99.4

REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), executed as of December 20, 2023, is made by and between (i) BlackRock Municipal Income Quality Trust, a closed-end fund organized as a Delaware statutory trust (the “Fund”) and (ii) DNT Asset Trust, a Delaware statutory trust organized and existing under the laws of the United States of America, including its successors and assigns by operation of law (“DNT”, or the “Shareholder”).

RECITALS

WHEREAS, the Fund and the Shareholder have entered into that certain Purchase Agreement dated as of December 20, 2023 (the “Purchase Agreement”), regarding the purchase of the VMTP Preferred Shares and certain other rights and obligations of the parties thereof as set forth therein and provide for the execution of this Agreement.

NOW THEREFORE, the Parties hereby agree to enter into to provide for certain registration rights as follows:

1. Certain Definitions. As used in this Agreement, the following terms have the following respective meanings:

“Aborted Registration” has the meaning set forth is Section 6(a) of this Agreement.

“Affiliate” means, with respect to any Person, any other Person directly or indirectly Controlling, Controlled by, or under common Control with such Person (including any subsidiary) and “Affiliates” shall have correlative meaning. For the purpose of this definition, the term “Control” (including with correlative meanings, the terms “Controlling”, “Controlled by” and “under common Control with”), as used with respect to any Person, shall mean the possession, directly or indirectly, of the power to direct or cause the direction of the management and policies of such Person, whether through the ownership of voting securities or by contract or otherwise.

“Agreement” has the meaning set forth in the preamble to this Agreement.

“BlackRock Persons” means the Fund, the Investment Adviser or any of their respective Affiliates.

“Blue Sky” means the statutes of any state regulating the sale of corporate securities within that state.

“Board” means the board of trustees of the Fund or any duly authorized committee thereof.

“Commission” means the United States Securities and Exchange Commission.

“Date of Original Issuance” has the meaning set forth in the Statement of Preferences.

“Demand Registration” has the meaning set forth in Section 3.1 of this Agreement.

“Designated Representative” has the meaning set forth in Section 6(j) of this Agreement.

“Effective Date” means the date of this Agreement.

“Exchange Act” means the United States Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder, all as from time to time in effect.

“FINRA” shall mean the Financial Industry Regulatory Authority or any successor.

“Form N-2” means such form under the Securities Act as in effect on the date hereof or any successor registration form under the Securities Act subsequently adopted by the Commission.

“Fund” has the meaning set forth in the preamble to this Agreement.

“Fund Indemnified Persons” has the meaning set forth in Section 7.2 of this Agreement.

“Holder” means any Person in whose name a VMTP Preferred Share is registered in the registration books of the Fund maintained by the Redemption and Paying Agent.

“Holder Indemnified Persons” means, with respect to each Holder, such Holder and its Affiliates and directors, officers, partners, employees, agents, representatives and control persons, entitled to indemnification by the Fund under Section 7 of this Agreement.

“Investment Adviser” means BlackRock Advisors LLC, or any successor investment adviser to the Fund.

“Liquidation Preference”, with respect to a given number of VMTP Preferred Shares, means U.S.$100,000 times that number.

“Majority Holders” means the Holder(s) of more than 50% of the Outstanding VMTP Preferred Shares.

“Outstanding” has the meaning set forth in the Statement of Preferences.

“Parties” means collectively the Fund and the Shareholder. Each of the Parties shall be referred to as a “Party.”

“Person” means and includes an individual, a partnership, a trust, a corporation, a limited liability company, an unincorporated association, a joint venture or other entity or a government or any agency or political subdivision thereof.

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“Prospectus” shall mean the final prospectus included in a Registration Statement, including any prospectus filed by the Fund under Rule 430A or Rule 424 of the rules and regulations of the Commission under the Securities Act in connection therewith, and any advertising or sales material prepared by the Fund and filed under Rule 482 of the rules and regulations of the Commission under the Securities Act in connection therewith, including in each such case all amendments and supplements to any such prospectus, advertising or sales material, and in each case including all material incorporated by reference therein.

“Public Offering” means an offering of Registrable Securities pursuant to an effective registration statement under the U.S. Securities Act of 1933, as amended.

“Purchase Agreement” has the meaning set forth in the recitals to this Agreement.

“Redemption and Paying Agent” has the meaning set forth in the Statement of Preferences.

“Registering Holders” has the meaning set forth in Section 3.1 to this Agreement.

“Registrable Securities” means (i) all of the VMTP Preferred Shares issued by the Fund on the Date of Original Issuance and that remains Outstanding and (ii) any VMTP Preferred Shares issued thereon as a dividend or other distribution.

“Registration” means a registration effected by preparing and filing a Registration Statement and the declaration or ordering of the effectiveness of that Registration Statement, and the terms “Register” and “Registered” have meanings correlative with the foregoing.

“Registration Expenses” means all expenses incurred by the Fund in complying with Section 3 of this Agreement, including, without limitation, all Registration, qualification, and filing fees, printing expenses, reasonable fees and disbursements of counsel for the Fund, reasonable fees and disbursements of one special counsel for all Holders (if different from counsels to the Fund), Blue Sky fees and expenses, the expense of any special audits or comfort letters incident to or required by a Registration. Registration Expenses do not include any underwriting discounts or commissions or any fees or expenses of counsel to the Holders.

“Registration Statement” means a registration statement prepared on Form N-2 under the Securities Act including the related final prospectus or prospectuses.

“Securities Act” means the United States Securities Act of 1933, as amended, and the rules and regulations of the Commission promulgated thereunder, all as from time to time in effect.

“Shareholder” has the meaning set forth in the preamble to this Agreement.

“Statement of Preferences” means the Statement of Preferences of the VMTP Preferred Shares.

“Underwriters’ Representative” has the meaning set forth in Section 3.3(b) of this Agreement.

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“U.S.$” or “USD” means United States dollars.

“VMTP Preferred Shares” means the shares of Series W-7 Variable Rate Muni Term Preferred Shares of the Fund, with par value of U.S. $0.001 per share and a liquidation preference of U.S. $100,000.

2. Registration Rights; Applicability of Rights. The Holders shall be entitled to the rights with respect to the Registration of the Registrable Securities set forth in this Agreement.

3. Demand Registration.

3.1. Request for Registration. If the Fund receives from the Shareholder a request in writing that the Fund effect a Registration with respect to all of the Registrable Securities, subject to the terms of this Agreement, the Fund shall (i) within 10 days of receipt of such written request, give written notice of the proposed Registration to all other Holders, and (ii) as soon as practicable, use its commercially reasonable efforts to effect Registration of the Registrable Securities (“Demand Registration”) to which the Fund has been requested to register by Holders thereof by written request given to the Fund within 15 days after receiving written notice from the Fund, subject to the limitations of this Section 3. Any such written demand for a Demand Registration shall specify the number of Registrable Securities proposed to be sold, if any, and the intended method(s) of distribution thereof. The right to request a Demand Registration is limited to the Shareholder, may only be exercised once during the term of this Agreement and must include all of the Registrable Securities; provided, that in the event of an Aborted Registration, the Shareholder shall be permitted to request one additional Demand Registration. Each other Holder of Registrable Securities, if any, must request that its shares be included in a Demand Registration (such Holders, together with the Shareholder, the “Registering Holders”), but may not independently request a Demand Registration; provided, that no such requesting Holder shall be obligated to sell any of its Registrable Securities in connection with the Registration. The substantive provisions of Section 3.3 of this Agreement shall be applicable to a Registration initiated under this Section 3.1.

3.2. Right of Deferral; Limitations.

(a) Notwithstanding the foregoing, the Fund shall not be obligated to file a Registration Statement pursuant to this Section 3 if the Fund furnishes to the Shareholder a certificate signed by the President or Chief Executive Officer or chairman of the Board stating that in the good faith judgment of the Board it would be materially detrimental to the Fund or its shareholders for a Registration Statement to be filed in the near future (including without limitation because the Fund is then engaged in a material transaction or has an undisclosed material corporate development, in either case, which would be required to be disclosed in the Registration Statement). In such event, the Fund’s obligation to use its commercially reasonable efforts to file a Registration Statement shall be deferred for a period not to exceed 120 days from the delivery of the certificate contemplated in the foregoing sentence to the Shareholder (the “Deferral Period”); provided, that the Fund shall not exercise the right to delay a request contained in this Section 3.2 more than once in any 12 month period, and provided further, that during the Deferral Period, the Fund shall not file a Registration Statement with respect to any preferred shares of the Fund other than a Registration Statement with respect to the sale of any preferred shares all or a portion of the proceeds of which will be used to redeem all of the Registrable Securities then Outstanding.

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(b) Notwithstanding anything herein to the contrary, the Fund shall not be obligated to effect a Registration of Registrable Securities if all of the Registrable Securities are not included in the Demand Registration.

(c) The Fund shall not be obligated to effect a Registration of Registrable Securities upon receipt of a written demand for a Demand Registration if the Fund has already completed a Demand Registration.

(d) The Fund shall not be obligated to effect a Registration of Registrable Securities upon receipt of a written demand for a Demand Registration if the Fund furnishes to the Shareholder a certificate signed by the President or Chief Executive Officer of the Fund stating that within 90 days of receipt of the written demand for a Demand Registration, the Fund intends to (i) file a Registration Statement and offer to the Shareholder and all other Holders the opportunity to register Registrable Securities thereunder in accordance with Section 3.1 or (ii) redeem all of the Registrable Securities Outstanding.

3.3. Underwriting in Demand Registration.

(a) Notice of Underwriting. If the Shareholder intends to distribute the Registrable Securities covered by its request by means of an underwriting, the Shareholder shall so advise the Fund as part of its request made pursuant to Section 3.1, and the Fund shall include that information in the written notice referred to in Section 3.1 of this Agreement. Each Holder shall have the right but not the obligation to include any or all of such Holder’s Registrable Securities in the underwriting to the extent provided herein; it being understood that a failure of all of the Registrable Securities of the Shareholder to be included in the Registration will result in the Fund not being required to complete the Registration.

(b) Selection of Underwriter in Demand Registration. The Fund shall (together with all Holders proposing to distribute their securities through the underwriting) enter into an underwriting agreement in customary form for an underwritten offering of preferred stock made solely by selling shareholders (the “Underwriting Agreement”) with the underwriter or, if more than one, the lead underwriter acting as the representative of the underwriters (the “Underwriters’ Representative”) selected for the underwriting by the Holders of a majority of the Registrable Securities proposed to be underwritten and with the consent of the Fund, such consent not to be unreasonably withheld. The Underwriting Agreement shall provide that in connection with the distribution of Registrable Securities pursuant to the underwriting, no purchaser (other than any underwriters acting as initial purchasers in the underwriting) shall be permitted to acquire more than 25% of the Outstanding VMTP Preferred Shares from the underwriters.

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(c) Marketing Limitation in Demand Registration. Notwithstanding any other provision of this Section 3, in the event the Underwriters’ Representative advises the Fund in writing that market factors (including, without limitation, the aggregate number of VMTP Preferred Shares requested to be Registered, the general condition of the market, and the status of the Persons proposing to sell securities pursuant to the Registration) require a limitation of the number of shares to be underwritten, then the Fund shall so advise the Designated Representative, and, if the Fund chooses to proceed with the Registration, the number of shares of Registrable Securities that may be included in the Registration and underwriting shall be allocated among all Holders of such Registrable Securities on a pro rata basis based on the number of Registrable Securities requested to be included in the Registration by all such selling Holders (including the Shareholder), provided, however, that the number of Registrable Securities to be included in any such underwriting held by Holders shall not be reduced unless all other Registrable Securities of the Fund, its Affiliates and BlackRock Persons, other than any account or Person that is an Affiliate of the Fund or a BlackRock Person solely because the Investment Adviser or its Affiliate is the investment adviser, manager, general partner of or otherwise exercises discretionary authority or control over such account or Person, are first entirely excluded from the underwriting. Unless the prior written consent of the Person holding a majority of the Registrable Securities to be included in the underwriting has been obtained, the number of the Registrable Securities included in any such underwriting shall not be reduced to less than 90% of the numbers of the Registrable Securities requested to be included. Any Registrable Securities or other securities excluded from the underwriting by reason of this Section 3.3(c) shall be withdrawn from the Registration. To facilitate the allocation of shares in accordance with the foregoing, the underwriters may round the number of shares allocated to any Holder to the nearest one share.

(d) Right of Withdrawal in Demand Registration. If any Holder of Registrable Securities (other than the Shareholder) desires, such Holder may elect to withdraw its Registrable Securities from sale thereunder in accordance with the Underwriting Agreement.

4. Expenses of Registration. All Registration Expenses incurred in connection with a Registration pursuant to Section 3.1 of this Agreement shall be split equally among the Fund and the Holders of Registrable Securities that are to be Registered; provided, that in the event of an Aborted Registration the Fund shall be obligated to pay 100% of any Registration Expenses incurred in connection with a subsequent Registration pursuant to Section 3.1 of this Agreement.

5. Assignability of Registration Rights; Termination of Registration Rights; Limitation on Subsequent Registration Rights

5.1. Assignability of Registration Rights. Except as provided in Section 8.11 of this Agreement, no Party may assign, delegate or otherwise transfer any of its rights or obligations under this Agreement without the prior written consent of the other Party to this Agreement.

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5.2. Termination of Registration Rights. The right to cause the Fund to register Registrable Securities granted under Section 3 of this Agreement and to receive notices pursuant to Section 3 of this Agreement, shall terminate on the earliest of (i) five months prior to the then current Term Redemption Date (as defined in the Statement of Preferences), (ii) a notice of redemption having been issued by the Fund under the Statement of Preferences for the redemption of all of the Registrable Securities, or the repurchase by the Fund of all of the Registrable Securities, (iii) the date the Shareholder is no longer the beneficial owner of any Outstanding VMTP Preferred Shares and (iv) the date a Demand Registration has been effected.

6. Registration Procedures and Obligations. To the extent within its control, the Fund shall use its commercially reasonable efforts, whenever required under this Agreement to effect the Registration of any Registrable Securities:

(a) (i) to prepare and file a Registration Statement with the Commission which (x) shall be on Form N-2, if available, or any other form for which the Fund qualifies or which counsel for the Fund shall deem appropriate and which form shall be available for the sale of all Registrable Securities to be registered thereunder in accordance with Section 3.1 above and the intended method(s) of distribution thereof (y) shall be available for the sale or exchange of the Registrable Securities in accordance with the intended method or methods of distribution by the selling Holders thereof and (z) shall comply in all material respects as to form with the requirements of the applicable form and include all financial statements required by the Commission to be filed therewith and all other information reasonably requested by the Underwriters’ Representative to be included therein relating to the underwriters and plan of distribution for the Registrable Securities, (ii) to cause such Registration Statement to become effective and remain effective for up to 60 days or, if earlier, until the Holder or Holders have completed the distribution thereto or withdrawn from such plan of distribution; provided, however, that the Fund shall not be required to cause a Registration Statement to remain effective for a period subsequent to 30 days after it became effective to the extent there are material events that in the opinion of counsel to the Fund require disclosure in the Registration Statement and the Fund has determined that any such additional disclosure is adverse to the interests of the Fund (the discontinuance of the effectiveness of the Registration Statement under any such circumstances, an “Aborted Registration”), (iii) cause the Registration Statement, as of the effective date of such Registration Statement, (x) to comply in all material respects with all applicable requirements of the Securities Act and (y) not to contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading and (iv) to cause the Prospectus, as of the date thereof, (x) to comply in all material respects with all applicable requirements of the Securities Act and (y) not to contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading;

(b) subject to Section 6(a) above, to prepare and file with the Commission such amendments and post-effective amendments to such Registration Statement as may be necessary to keep such Registration Statement effective for the period specified in Section 6(a)(ii); cause the Prospectus to be supplemented by any required prospectus supplement, and as so supplemented to be filed pursuant to applicable rules under the Securities Act; and comply in all material respects with the applicable provisions of the Securities Act with respect to the disposition of all Registrable Securities covered by the Registration Statement during the period specified in Section 6(a)(ii) in accordance with the intended method or methods of distribution by the selling Holders thereof, as set forth in the Registration Statement;

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(c) to furnish to each Holder for which the Registrable Securities are being registered and to each underwriter of an underwritten offering of the Registrable Securities, if any, as many copies of the Prospectus, any preliminary prospectus, and any amendments or supplements thereto as such Holder or underwriter may reasonably request in order to facilitate the public sale or other disposition of the Registrable Securities; the Fund hereby consents to the use of the Prospectus and any preliminary prospectus approved by the Fund in writing for such use, by each Holder for which the Registrable Securities are being registered and each underwriter of an underwritten Public Offering of the Registrable Securities, if any, in connection with the offering and sale of the Registrable Securities covered by the Prospectus or any preliminary prospectus, as applicable;

(d) (i) to register or qualify the Registrable Securities, no later than the time the applicable Registration Statement is declared effective by the Commission, under all applicable state securities or Blue Sky laws of such United States jurisdictions as the Underwriters’ Representative, if any, or any Holder having Registrable Securities covered by the Registration Statement, shall reasonably request and (ii) to keep each such registration or qualification effective during the period specified in Section 6(a)(ii);

(e) to notify the Designated Representative promptly, and, if requested by such the Designated Representative, confirm such notification in writing, (i) when the Registration Statement has become effective and when any post-effective amendments and supplements thereto become effective, (ii) when the Fund discovers the issuance by the Commission or any state securities authority of any stop order, injunction or other order or requirement suspending the effectiveness of such Registration Statement or the initiation of any proceedings for that purpose, (iii) if the Fund receives any notification with respect to the suspension of the qualification of the Registrable Securities for sale in any jurisdiction or the initiation of any proceeding for such purpose and (iv) when the Fund discovers the happening of any event during the period the Registration Statement is effective as a result of which such Registration Statement or the Prospectus contains any untrue statement of a material fact or omits to state any material fact required to be stated therein or necessary to make the statements therein, in light of the circumstances under which they were made, not misleading;

(f) to furnish designated counsel for each of the underwriters, if any, and for the Holders for which the Registrable Securities are being registered, copies of any request by the Commission or any state securities authority for amendments or supplements to a Registration Statement and Prospectus or for additional information;

(g) to obtain the withdrawal of any order suspending the effectiveness of a Registration Statement at the earliest possible time;

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(h) upon request, to furnish to the Underwriters’ Representative of an underwritten Public Offering of the Registrable Securities, if any, without charge, at least one signed copy of such Registration Statement and any post-effective amendment thereto, including financial statements and schedules, all documents incorporated therein by reference and all exhibits; and furnish to each Holder upon request for which the Registrable Securities are being registered, at least one conformed copy of the Registration Statement and any post-effective amendment thereto (without documents incorporated therein by reference or exhibits thereto, unless requested);

(i) upon the Fund’s discovery of the occurrence of any event contemplated by paragraph (e)(iv) of this Section, to prepare a supplement or post-effective amendment to the Registration Statement or the related Prospectus, or any document incorporated therein by reference, or file any other required document so that, as thereafter delivered to the purchasers of the Registrable Securities, the Prospectus will not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading;

(j) to enter into customary agreements (including, in the case of an underwritten Public Offering, underwriting agreements in customary form for sales only by selling shareholders, and including customary provisions with respect to indemnification and contribution or as otherwise agreed by the parties) and in connection therewith:

(i) in the case of an underwritten Public Offering, to make such representations and warranties to the underwriters in form, substance and scope as are customarily made by issuers to underwriters in similar underwritten offerings for sales only by selling shareholders;

(ii) in the case of an underwritten Public Offering, to obtain an opinion of counsel to the Fund and updates thereof addressed to the underwriters covering the matters customarily covered in opinions requested in similar underwritten offerings for sales only by selling shareholders and such other matters as may be reasonably requested by underwriters (and which opinion (in form, scope and substance) shall be reasonably satisfactory to the Underwriters’ Representative, if any); provided, that the Holders and their counsel shall be entitled to rely upon certificates delivered by the Fund to counsel in connection with the opinions referenced in this subclause (ii);

(iii) in the case of an underwritten Public Offering, to obtain “comfort” letters or “agreed-upon procedures” letters and updates thereof from the Fund’s independent certified public accountants addressed to the underwriters which letters shall be customary in form and shall cover matters of the type customarily covered in such letters to underwriters in connection with similar underwritten offerings for sales only by selling shareholders; and

(iv) deliver such customary documents and certificates as may be reasonably requested by a designated representative of the Majority Holders of the Registrable Securities being sold (the “Designated Representative”) or by the Underwriters’ Representative, if any;

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(k) to make available for inspection by the Designated Representative and by any underwriters participating in any disposition pursuant to the Registration Statement and counsel or accountants retained by such Holders or by counsel to such underwriters, all relevant and material financial and other records, pertinent and material corporate documents and properties of the Fund, except to the extent prohibited by law or regulation and cause the respective officers, directors and employees of the Fund to supply all material information reasonably requested by such Designated Representative, underwriter, counsel or accountant in connection with such Registration Statement to the extent that such requests do not interfere with the discharge of such person’s duties; provided, that, prior to the Fund or its representatives providing any such documentation or information, in each case, each Registering Holders and each underwriter shall have entered into a confidentiality agreement with the Fund in form and substance reasonably satisfactory to the Fund;

(l) within a reasonable time prior to the filing of the Registration Statement, any Prospectus, any amendment to the Registration Statement or amendment or supplement to a Prospectus, to provide copies of such document to the selling Holders of the Registrable Securities and to counsel to such Holders and to the underwriter or underwriters of a underwritten Public Offering of the Registrable Securities, if any; to fairly consider such reasonable changes in any such document prior to or after the filing thereof as the counsel to the Holders or the underwriter or the underwriters may request and make such of the representatives of the Fund as shall be reasonably requested by the Designated Representative or the Underwriters’ Representative available for discussion with such person of such document;

(m) to comply in all material respects with all applicable rules and regulations of the Commission;

(n) to cooperate with any reasonable requests made in connection with any filings required to be made with FINRA and in the performance of any due diligence investigation by any underwriter in an underwritten offering in accordance with Section 6(k); and

(o) to facilitate the distribution and sale of any Registrable Securities to be offered pursuant to this Agreement by taking such actions as shall be reasonably requested by the Underwriters’ Representative.

Each selling Holder of the Registrable Securities as to which a Registration is being effected pursuant to this Agreement must agree, as a condition to the Registration obligations provided herein, to furnish to the Fund such information regarding such Holder required to be included in the Registration Statement, the ownership of the Registrable Securities by such Holder (including information on the Persons having voting and dispositive control thereof) and the proposed distribution by such Holder of such Registrable Securities as the Fund may from time to time reasonably request in writing. Each selling Holder of the Registrable Securities as to which a Registration is being effected pursuant to this Agreement must agree, as a condition to the Registration obligations provided herein, to suspend use of any Prospectus if it has received the notification contemplated by Section 6(e)(iv) above until such time as the Fund notifies such Holder that it has complied with Section 6(i) above.

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7. Indemnification.

7.1. Fund’s Indemnification of Holders. The Fund agrees to indemnify and hold harmless each Holder Indemnified Person from and against any losses, claims, damages, liabilities or expenses incurred by them (including reasonable fees and disbursements of outside counsel) which are related to or arise out of any untrue or alleged untrue statement of a material fact contained in a Registration Statement, any Prospectus or in any amendment or supplement thereto, or arise out of or relate to any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein (in the case of any Prospectus or supplement thereto, in light of the circumstances under which they were made) not misleading, except insofar as such loss, claim, damage, liability or expense arises out of or is based upon (a) any untrue statement or allegedly untrue statement or omission or alleged omission made in such Registration Statement, Prospectus or supplement thereto in reliance upon and in conformity with information furnished in writing to the Fund by the underwriter or any Holder expressly for use therein, or (b) the use of a Registration Statement or Prospectus during a period when the Designated Representative has been notified that a stop order has been issued in respect thereof or any proceeding for that purpose has been initiated, or the use of a Registration Statement or Prospectus has been suspended by the Fund pursuant to the terms of this Agreement. The foregoing indemnity shall not inure to the benefit of any Holder Indemnified Person from whom the person asserting losses, claims, damages, liabilities or expenses purchased Registrable Securities, if a copy of the Prospectus (as then amended or supplemented if the Fund shall have furnished any amendments or supplements thereto) was not sent or given by or on behalf of such Holder Indemnified Person to such person, if required by law so to have been delivered at or prior to the written confirmation of the sale of Registrable Securities to such person, and if the Prospectus (as so amended or supplemented) would have cured the defect giving rise to such losses, claims, damages, liabilities or expenses, unless such failure is the result of noncompliance by the Fund with Section 6(b) of this Agreement.

7.2. Holders’ Indemnification of the Fund. Each Holder will, with respect to a Registration Statement where Registrable Securities were registered under the Securities Act, indemnify and hold harmless the Fund, each of the Fund’s directors and officers, and each other person, if any, who controls the Fund (within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act) (each, a “Fund Indemnified Persons”), against any losses, claims, damages, liabilities or expenses, whether joint or several, insofar as such losses, claims, damages, liabilities or expenses (or actions in respect thereof) arise out of or are based upon any untrue statement or allegedly untrue statement of a material fact contained in a Registration Statement under which the sale of such Registrable Securities was registered under the Securities Act, any Prospectus or supplement thereto contained in such Registration Statement, or any amendment or supplement to the Registration Statement, or arise out of or are based upon any omission or the alleged omission to state a material fact required to be stated therein or necessary to make the statement therein not misleading, if the statement or omission was made in reliance upon and in conformity with information furnished in writing to the Fund by the Holder expressly for use therein. Each Holder’s indemnification obligations hereunder shall be limited to the amount of any net proceeds actually received by such Holder.

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7.3. Indemnification Procedure. If any action, suit, proceeding or investigation shall be brought or asserted against any indemnified person, such indemnified person shall, if a claim in respect thereof is to be made against any indemnifying person under this Section 7, notify the indemnifying person in writing with reasonable promptness. The failure to deliver written notice to the indemnifying person within a reasonable time of the commencement of any such action, if materially prejudicial to its ability to defend such action, shall relieve such indemnifying person of any liability to the indemnified party under this Section 7, but the omission so to deliver written notice to the indemnifying person shall not relieve it of any liability that it may have to any indemnified party otherwise than under this Section 7. The indemnifying person shall be entitled to assume the defense of any such action, suit, proceeding or investigation, including the employment of counsel reasonably satisfactory to the indemnified person. The indemnified person shall have the right to separate counsel of its own choice to represent it, but the fees and expenses of such counsel shall be at the expense of such indemnified person unless (i) the indemnifying person has failed promptly to assume the defense and employ counsel reasonably satisfactory to the indemnified person in accordance with the preceding sentence or (ii) the indemnified person shall have been advised by counsel that there exist actual or potential conflicting interests between the indemnifying person and such indemnified person, including situations in which one or more legal defenses may be available to such indemnified person that are different from or additional to those available to the indemnifying person.

The indemnifying person shall not be liable for any settlement of any such Proceeding effected without its prior written consent. The indemnifying person will not, without the prior written consent, which consent shall not be unreasonably withheld, conditioned or delayed, of the indemnified persons, settle or compromise or consent to the entry of any judgment in any pending or threatened claim, action, suit or proceeding in respect of which indemnification may be sought by the indemnified persons hereunder (whether or not the indemnifying person is an actual or potential party to such claim, action, suit or proceeding) unless such settlement, compromise or consent includes an unconditional release of each indemnified person from all liability and obligations arising therefrom.

7.4. Contribution. To the extent that the indemnification sought by indemnified persons pursuant to this Agreement is unavailable to an indemnified person or insufficient in respect of any losses, claims, damages or liabilities (or actions in respect thereof), then the indemnifying person, in order to provide for just and equitable contribution and in lieu of indemnifying such indemnified person, shall contribute to the amount paid or payable by such indemnified persons as a result of such losses, claims, liabilities, damages and expenses (or actions in respect thereof) in such proportion as is appropriate to reflect the relative fault of the indemnifying person on the one hand and the indemnified person(s) on the other, as well as any other relevant equitable considerations. No person found liable for a fraudulent misrepresentation shall be entitled to contribution from any person who is not also found liable for such fraudulent misrepresentation. The indemnity, reimbursement and contribution obligations under this Agreement shall be in addition to any rights that any indemnified person may have at common law or otherwise.

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7.5. No Limitations. Nothing in this Section 7 is intended to limit any party’s obligations contained in other parts of this Agreement or the VMTP Preferred Shares, provided that no amount shall be reimbursed twice in any event.

7.6. Conflicts. Notwithstanding the foregoing, to the extent that provisions on indemnification and contribution contained in the Underwriting Agreement entered into in connection with the underwritten public offering are in conflict with the foregoing provisions, the provisions in the Underwriting Agreement shall control.

8. Miscellaneous.

8.1. Governing Law. This Agreement shall be construed in accordance with and governed by the domestic law of the State of New York.

THE PARTIES HERETO HEREBY SUBMIT TO THE NON-EXCLUSIVE JURISDICTION OF THE FEDERAL AND NEW YORK STATE COURTS LOCATED IN THE CITY OF NEW YORK IN CONNECTION WITH ANY DISPUTE RELATED TO THIS AGREEMENT OR ANY MATTERS CONTEMPLATED HEREBY.

8.2. No Waivers. No failure or delay by the Fund or the Shareholder in exercising any right, power or privilege hereunder or under the VMTP Preferred Shares shall operate as a waiver thereof nor shall any single or partial exercise thereof preclude any other or further exercise thereof or the exercise of any other right, power or privilege. No failure or delay by the Fund or the Shareholder in exercising any right, power or privilege under or in respect of the VMTP Preferred Shares shall affect the rights, powers or privileges of the Fund or the Shareholder hereunder or shall operate as a limitation or waiver thereof. The rights and remedies herein provided shall be cumulative and not exclusive of any rights or remedies provided by law.

8.3. Specific Performance. Each Party hereby acknowledges that the remedies at law of the other Party for a breach or threatened breach of this Agreement would be inadequate and, in recognition of this fact, any Party, without posting any bond, and in addition to all other remedies that may be available, shall be entitled to seek equitable relief in the form of specific performance, injunctions or any other equitable remedy.

8.4. Waiver of Jury. The Fund and the Shareholder hereby waive trial by jury in any action, proceeding or counterclaim brought by either of the parties hereto against the other on any matters whatsoever arising out of or in any way connected with this Agreement.

8.5. Counterparts and Facsimile Execution. This Agreement may be signed in counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument. Any counterpart or other signature delivered by facsimile or electronic mail shall be deemed for all purposes as being a good and valid execution and delivery of this Agreement by that party.

The exchange of copies of this Agreement and of signature pages that are executed by manual signatures that are scanned, photocopied or faxed or by other electronic signing created on an electronic platform (such as DocuSign) or by digital signing (such as Adobe Sign) that is approved by the parties hereto, shall constitute effective execution and delivery of this Agreement

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for all purposes. Signatures of the parties hereto that are executed by manual signatures that are scanned, photocopied or faxed or by other electronic signing created on an electronic platform (such as DocuSign) or by digital signing (such as Adobe Sign) that is approved by the parties hereto shall be deemed to be their original signatures for all purposes of this Amendment as to the parties hereto and may be used in lieu of the original.

Anything in this Agreement or the VMTP Preferred Shares certificate to the contrary notwithstanding, for the purposes of the transactions contemplated by this Agreement, the VMTP Preferred Shares certificate and any document to be signed in connection with this Agreement (including the VMTP Preferred Shares certificate and amendments, supplements, waivers, consents and other modifications and issuance and delivery documents) or the transactions contemplated hereby may be signed by manual signatures that are scanned, photocopied or faxed or other electronic signatures created on an electronic platform (such as DocuSign) or by digital signature (such as Adobe Sign) that is approved by the parties hereto, and contract formations on electronic platforms approved by the parties hereto, and the keeping of records in electronic form, are hereby authorized, and each shall be of the same legal effect, validity or enforceability as a manually executed signature in ink or the use of a paper-based recordkeeping system, as the case may be.

8.6. Headings. The headings of the Sections of this Agreement are for convenience and shall not by themselves determine the interpretation of this Agreement.

8.7. Notices. All notices, requests and other communications to any Party hereunder shall be in writing (including telecopy, electronic mail or similar writing), and shall be given to such party at its address or telecopy number or email address set forth below or such other address or telecopy number or email address as such party may hereafter specify for the purpose by notice to the other parties. Each such notice, request or other communication shall be effective when delivered at the address specified in this Section. The notice address for each party is specified below:

If to the Fund, to:

BlackRock Municipal Income Quality Trust

100 Bellevue Parkway

Wilmington, DE 19808-3700

Attention: Accounting Custody

Telephone: (302) 797-6368

Facsimile: (302) 797-2455

Email: Accounting.Custody@blackrock.com

If to DNT, to:

DNT Asset Trust

383 Madison Avenue, Floor 3

New York, NY 10179

Attention: Sean Saroya

Telephone: (212) 834-3430

Email: sean.b.saroya@jpmorgan.com

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8.8. Amendments and Waivers. Any provision of this Agreement may be amended or waived if, but only if, such amendment or waiver is in writing and is signed by the Fund and the Holders of not less than a majority of the Registrable Securities (calculated on an as-converted basis).

8.9. Severability. In case any provision of this Agreement shall be invalid, illegal, or unenforceable, the validity, legality, and enforceability of the remaining provisions shall not in any way be affected or impaired thereby so long as the intent of the Parties to this Agreement be preserved.

8.10. Entire Agreement. This Agreement shall constitute the entire agreement and understanding between the parties hereto with respect to the matters set forth herein and shall supersede any and all prior agreements and understandings relating to the subject matter hereof.

8.11. Successors and Assigns; Assignment. The provisions of this Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns. Neither the Fund nor the Shareholder may assign or otherwise transfer any of its rights or obligations under this Agreement, without the prior written consent of the other Party (other than by merger or operation of law) except that prior to the VMTP Preferred Shares being registered under the Securities Act, any transferee of VMTP Preferred Shares in a valid transfer recognized by or required to be recognized by the Fund shall have the rights of a Holder hereunder. Any assignment without such prior written consent shall be void.

8.12. Effectiveness of this Agreement. This Agreement shall be effective as of the Effective Date and the rights and obligations of the Parties contained herein in each case shall be binding as of the Effective Date. Notwithstanding anything expressed or implied in this Agreement to the contrary, nothing in this Agreement shall confer upon any Holder any rights to dividends on, or a redemption of, VMTP Preferred Shares (other than the rights provided to Holders under the Statement of Preferences) or any rights which would result in the VMTP Preferred Shares owned or held by such Holder having priority over VMTP Preferred Shares owned or held by any other person as to distribution of assets or payment of dividends.

[Signatures follow on the next page.]

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IN WITNESS WHEREOF, the parties to this Agreement have executed this Agreement on the date first written above.

THE FUND:
BLACKROCK MUNICIPAL INCOME QUALITY TRUST
By:	/s/ Jonathan Diorio
Name: Jonathan Diorio
Title: Vice President
THE SHAREHOLDER:
DNT ASSET TRUST
By:	/s/ Timothy Bittel
Name: Timothy Bittel
Title: Authorized Officer

[Signature Page to the Registration Rights Agreement]