BlackRock MuniYield Quality Fund III, Inc. (the "Fund")
                              File No. 811-06540
  Item No. 77Q1(a) (Copies of Material Amendments to Registrant's Charter or
                            By-laws) -- Attachment

Attached please find as an exhibit under Sub-Item 77Q1(a) of Form N-SAR, a copy
of the Fund's Amendment to the Notice of Special Rate Period of the Fund's
Variable Rate Demand Preferred Shares filed with the books and records of the
Fund on June 7, 2016.

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                                                                Exhibit 77Q1(a)

                  BLACKROCK MUNIYIELD QUALITY FUND III, INC.
                                 (THE "FUND")
                                  SERIES W-7
             VARIABLE RATE DEMAND PREFERRED SHARES ("VRDP SHARES")

                             CUSIP NO. 09254E863*

                  AMENDMENT TO NOTICE OF SPECIAL RATE PERIOD

                                    June 7, 2016

                                    BlackRock MuniYield Quality Fund III, Inc.
                                    100 Bellevue Parkway
                                    Wilmington, Delaware 19809

TO: Addressees listed on Schedule 1 hereto

   In accordance with the Fund's Articles Supplementary Establishing and Fixing
the Rights and Preferences of Variable Rate Demand Preferred Shares, dated
May 17, 2011 (the "ARTICLES SUPPLEMENTARY"), the Fund hereby notifies the
Liquidity Provider, the Remarketing Agent and the Holders of the VRDP Shares
that the last day of the Special Rate Period has been extended from June 22,
2016 to June 21, 2017 in accordance with the terms of the Notice of Special
Rate Period, dated June 20, 2012 (the "NOTICE OF SPECIAL RATE PERIOD").

   The last day of the Special Rate Period shall be June 21, 2017, or such
later date as the Special Rate Period may be extended pursuant to the terms of
the Notice of Special Rate Period.

   Capitalized terms used but not defined in this Amendment to Notice of
Special Rate Period shall have the meanings given to such terms in the Articles
Supplementary and the Notice of Special Rate Period.

                           [Signature Page Follows]

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* NOTE: Neither the Fund nor the Tender and Paying Agent shall be responsible
  for the selection or use of the CUSIP Numbers selected, nor is any
  representation made as to its correctness indicated in any notice or as
  printed on any VRDP Share certificate. It is included solely as a convenience
  to Holders of VRDP Shares.

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IN WITNESS WHEREOF, I have signed this Amendment to the Notice of Special Rate
Period as of the date first written above.

                                     BLACKROCK MUNIYIELD QUALITY FUND III, INC.

                                     By:  /s/ Jonathan Diorio
                                          --------------------------------------
                                          Name:   Jonathan Diorio
                                          Title:  Vice President

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                                                                     SCHEDULE 1

               RECIPIENTS OF THIS NOTICE OF SPECIAL RATE PERIOD

Citibank, N.A.
390 Greenwich Street, 2nd Floor
New York, New York 10013
Attention: MSD Middle Office Manager
Telephone: (212) 723-6320
Fax: (212) 723-8642
Email: msdcititob@citi.com

Citigroup Global Markets Inc.
390 Greenwich Street
New York, New York 10013
Attention: Middle Office Manager
Telephone: (212) 723-7124
Fax: (212) 723-8642
Email: msdcititob@citi.com

The Depository Trust Company
LensNotice@dtcc.com