P O W E R O F A T T O R N E Y
                                   SECTION 16


         The undersigned, Joseph H. Bryant, hereby:

          l.  Employs,  appoints,  authorizes,  empowers,  and  constitutes  the
     Corporate   Secretary  of  Unocal  Corporation,   a  Delaware   corporation
     ("Unocal"),  or any duly appointed  Assistant Secretary of Unocal, and each
     of them as his true and lawful attorneys-in-fact to:

         (a)      fill out and file and execute on his behalf certain reporting
                  forms known as Form 3, Form 4, and Form 5, and any amendments
                  and corrections thereto, or any other forms prescribed by the
                  Securities and Exchange Commission (or other authorities)
                  under Section 16(a) of the Securities Exchange Act of 1934
                  (the "Act"), as amended, as such forms pertain to his holdings
                  of securities in Unocal; and

         (b)      do and perform all things incident, necessary and proper to
                  appropriately complete, execute and file said forms, and in
                  conjunction therewith to do all things which in the opinion of
                  the attorney(s)-in-fact may be of benefit to, in the best
                  interest of, or legally required by, the undersigned.

          2. Grants to each such attorney-in-fact full power and authority to do
     and perform all and every act and thing  whatsoever  requisite,  necessary,
     and  proper to be done in the  exercise  of any of the  rights  and  powers
     herein   granted,   as  fully  to  all   intents   and   purposes  as  such
     attorney-in-fact  might or could do if personally present,  with full power
     of substitution  and revocation,  hereby  ratifying and confirming all that
     such attorney-in-fact,  or his substitute or substitutes, shall lawfully do
     or cause to be done by virtue of this Power of Attorney  and the rights and
     powers herein granted.

          3.  Represents and warrants to Unocal and to its  directors,  officers
     and the  attorneys-in-fact  appointed  hereby,  that the  undersigned  will
     provide full,  accurate,  and timely information to them, in the detail and
     at the  frequency  which they may  demand,  as to his  direct and  indirect
     interests in Unocal securities, as well as any changes therein, in order to
     enable  them  to  assist  the   undersigned  in  fulfilling  the  reporting
     requirements of Section 16(a) of the Act.

          4.  Acknowledge  that the foregoing  attorneys-in-fact,  in serving in
     such capacity at the request of the undersigned,  are not assuming,  nor is
     Unocal assuming,  any of the undersigned's  responsibilities to comply with
     Section 16 of the Securities and Exchange Act of 1934.

          5. This Power of Attorney  shall remain in effect  until  revoked in a
     signed writing by the undersigned delivered to the Corporate Secretary.

                                                     /S/ Joseph H. Bryant
                                                  ----------------------------
                                                          Signature

     DATED: August 13, 2004