Exhibit 23.3

                       CONSENT OF INDEPENDENT ACCOUNTANTS




The Board of Directors
Pure Resources, Inc.

     We consent to incorporation by reference in the registration statement
(No. 333-99147) on Form S-4 of Unocal Corporation of our report dated February
14, 2002, except for Note 22 which is dated July 26, 2002, relating to the
consolidated balance sheet of Pure Resources, Inc. and subsidiaries as of
December 31, 2001 and 2000 and the related consolidated statements of
operations, stockholders' equity and owner's net investment and cash flows for
the years then ended, which report appears in the December 31, 2001 annual
report on Form 10-K/A Amendment No. 1 of Pure Resources, Inc. Our report refers
to a change in accounting for derivative instruments and hedging activities.


                                                  KPMG LLP


Midland, Texas
September 18, 2002