Exhibit 23.3

                       CONSENT OF INDEPENDENT ACCOUNTANTS

The Board Of Directors
Unocal Corporation

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 sheeet 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.


                                        /s/ KPMG LLP

                                        KPMG LLP

Midland, Texas
November 6, 2002