EXHIBIT 10


                       AMENDMENT No. 2 TO RIGHTS AGREEMENT

                 AMENDMENT No. 2 TO RIGHTS AGREEMENT, dated as of August 2,
2002, (this "Amendment"), to the Rights Agreement, dated as of January 5, 2000
(the "Rights Agreement"), by and between Unocal Corporation (the "Company") and
Mellon Investor Services LLC, a New Jersey limited liability company (as
successor to ChaseMellon Shareholder Services, L.L.C.), as Rights Agent (the
"Rights Agent"), as amended by the Amendment to Rights Agreement, dated as of
March 27, 2002 (the "First Amendment"). Terms used herein but not defined shall
have the meaning assigned to them in the Rights Agreement as amended.

                 WHEREAS, the Company and the Rights Agent have heretofore
executed and entered into the Rights Agreement; and

                 WHEREAS, the Company and the Rights Agent have heretofore
executed and entered into the First Amendment; and

                 WHEREAS, pursuant to Section 27 of the Rights Agreement, the
Company may from time to time supplement or amend the Rights Agreement in
accordance with the provisions of such Section 27; and

                 WHEREAS, the Board of Directors of the Company has determined
that it is in the best interest of the Company and its stockholders to amend the
Rights Agreement to provide that any "Person" that is a "Qualified Institutional
Investor" (as defined herein) will not be deemed an "Acquiring Person."

                 NOW, THEREFORE, the Company and the Rights Agent hereby amend
the Rights Agreement as follows:

                  1.  Section 1 of the Rights  Agreement  is hereby  amended  to
revise  and  restate  in its  entirety  the  following definition:

                           (p) "Qualified Institutional Investor" shall mean, as
                  of any time of determination, a Person that is described in
                  Rule 13d-l(b)(1) promulgated under the Exchange Act (as such
                  Rule is in effect on the date hereof) and is eligible to
                  report (and, if such Person is the Beneficial Owner of greater
                  than 5% of the Common Shares of the Company, does in fact
                  report) beneficial ownership of Common Shares of the Company
                  on Schedule 13G, and such Person (i) is not required to file a
                  Schedule 13D (or any successor or comparable report) with
                  respect to its beneficial ownership of Common Shares of the
                  Company, (ii) shall be the Beneficial Owner of less than 15%
                  of the Common Shares of the Company then outstanding
                  (including in such calculation the holdings of all of such
                  Person's Affiliates and Associates other than those which,
                  under published interpretations of the SEC or its Staff, are
                  eligible to file separate reports on Schedule 13G with respect
                  to their beneficial ownership of the Common Shares of the
                  Company) and (iii) shall be the Beneficial Owner of less than
                  25% of the Common Shares of the Company then outstanding.

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                  2. Exhibit B to the Rights Agreement, being the form of Rights
Certificate, is hereby modified and amended by inserting in the third line of
the first paragraph following the words "dated as of January 5, 2000, as amended
as of March 27, 2002" the words "and as of August 2, 2002".

                  3. This Amendment shall be deemed to be a contract made under
the laws of the State of Delaware and for all purposes shall be governed by and
construed in accordance with the laws of such State applicable to contracts made
and performed entirely within such State; provided, however, that all provisions
regarding the rights, duties and obligations of the Rights Agent shall be
governed by and construed in accordance with the laws of the State of New York
applicable to contracts made and to be performed entirely within such State.

                  4. Except as specifically amended by this Agreement, all other
terms and conditions of the Rights Agreement, as amended by the First Amendment,
shall remain in full force and effect and are hereby ratified and confirmed.

                  5. This Amendment may be executed in any number of
counterparts and each of such counterparts shall for all purposes be deemed an
original, and all such counterparts shall together constitute but one and the
same instrument.

                  IN WITNESS WHEREOF, this Amendment has been duly executed by
the Company and the Rights Agent as of the day and year first written above.



Attest:                                   UNOCAL CORPORATION



By:  /s/BRIGITTE M. DEWEZ                 By:   /s/DENNIS P. R. CODON
   --------------------------------           ----------------------------------
    Name:    Brigitte M. Dewez                 Name:   Dennis P.R. Codon
    Title:   Corporate Secretary               Title:  Senior Vice President,
                                                       General Counsel & Chief
                                                       Legal Officer


Attest:                                   MELLON INVESTOR SERVICES LLC
                                               (as Rights Agent)



By:  /s/SHARON KNEPPER                    By:   /s/JAMES KIRKLAND
   --------------------------------           ----------------------------------
    Name:    Sharon Knepper                    Name:   James Kirkland
    Title:   Vice President                    Title:  Assistant Vice President

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