EXHIBIT 10.4

                               UNOCAL CORPORATION

                      2000 EXECUTIVE STOCK PURCHASE PROGRAM

     THIS AWARD AGREEMENT (this "Agreement") dated March 16, 2000
is between Unocal Corporation,  a Delaware corporation (the "Company"),  and the
Participant named below and constitutes the agreement of the parties as follows:
the Company  agrees to loan to the  Participant  the amount set forth below (the
"Loan") to  purchase  and pay for  shares of Common  Stock of the  Company  (the
"Common  Stock") in the open market,  such  purchase to commence on the date set
forth below,  subject to the terms and conditions  hereof (this  "Award").  This
Award is granted pursuant to and subject to the terms of the Unocal  Corporation
2000  Executive  Stock  Purchase  Program (the  "Program"),  attached  hereto as
Exhibit A, and any rules or guides to  administration  adopted from time to time
by the  Management  Development  and  Compensation  Committee  or any  successor
committee  appointed  by the  Company's  Board of Directors  to  administer  the
Program (the "Committee").  The Participant's obligation to repay the Loan shall
be evidenced by a full recourse note, in the form attached  hereto as Exhibit B,
executed by the Participant and delivered to the Company on the Purchase Date. A
signed facsimile shall be deemed acceptable delivery.

Participant:      Charles R. Williamson

Loan Amount:      $5,000,000

Purchase Date(s)
Commencement:     March 16, 2000



     The Participant represents, warrants and agrees as follows:

     1. The proceeds of the Loan will be used solely for the business purpose of
purchasing shares of the Common Stock;

     2. The Loan is not being taken for personal, family or household purposes;

     3. The  taking  and  repayment  of the  Loan  will not  violate  any  other
agreement to which the  Participant  is a party or by which the  Participant  is
bound;

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     4. The  Participant  is not in  possession of any  undisclosed  information
concerning  the Company which,  if disclosed,  would be material to investors in
the Common Stock; and

     The  Participant  understands  that  purchases,  sales and ownership of the
Common Stock are subject to the  requirements  of the Securities Act of 1933 and
the Securities  Exchange Act of 1934 and agrees to comply with such laws and the
rules and regulations thereunder, including without limitation,  restrictions on
the  ability of  affiliates  of the  Company  to sell the  Common  Stock and the
reporting requirements of Section 16 of the Securities Exchange Act of 1934.



UNOCAL CORPORATION                                      AGREED AND ACKNOWLEDGED:
(a Delaware corporation)


By:   /s/DENNIS P.R. CODON                             /s/CHARLES R. WILLIAMSON
     -------------------------                         -------------------------
Its:  Vice President, Chief Legal Officer              Participant's Signature
      and General Counsel

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<PAGE>

                                                                       EXHIBIT B

                                  FULL RECOURSE
                                 PROMISSORY NOTE
                               DUE MARCH 16, 2008

$5,000,000                                                        March 16, 2000
----------

     FOR  VALUE  RECEIVED,  Charles  R.  Williamson,  an  individual  ("Maker"),
unconditionally  promises to pay to Unocal Corporation,  a Delaware  corporation
(together  with any  successor  or assignee by  operation  of law or  otherwise,
"Payee"),  on the  earlier  of March 16,  2008 or such  other  date as  provided
herein,  in the  manner  and at  the  place  hereinafter  provided,  the  unpaid
principal  amount of all  advances  made by Payee to Maker for the  purposes  of
Maker's  purchase of common  stock of Payee  pursuant to the terms of the Unocal
Corporation 2000 Executive Stock Purchase Program (the "Program").  All advances
made under this Note shall be noted hereon; provided,  however, that the failure
to make a notation shall not limit or otherwise  affect the obligations of Maker
hereunder with respect to payments of principal or interest on this Note.

     The  initial  principal  amount  of  this  Note  is  five  million  dollars
($5,000,000). Such principal amount shall be increased by an amount equal to any
accrued but unpaid  interest as set forth in the next paragraph of this note and
decreased by any of the funds not used to purchase  shares under the Program and
by any repayments of principal.  The principal  amount  outstanding on March 16,
2005, shall be payable in three equal annual installments on the March 16, 2006,
March 16, 2007 and at maturity.

     Maker also promises to pay interest on the unpaid  principal amount of this
Note from the date such  principal is advanced  until such  principal is paid in
full at a rate  per  annum  equal  to the  lesser  of:  (i) the  maximum  amount
allowable pursuant to applicable law; or (ii) 6.8%.  Interest on this Note shall
be computed on the basis of a 365-day  year,  based on the actual number of days
elapsed. Interest shall be payable in arrears [annually] on the sixteenth (16th)
day of each March (an "Interest  Payment  Date"),  commencing on March 16, 2001,
upon any  prepayment  of this Note (to the extent  accrued  on the amount  being
prepaid) and at maturity; provided that, prior to March 17, 2005, interest shall
be payable  only in an amount  equal to  dividends  paid on the shares of Common
Stock of Payee purchased for Maker under the Program,  subject to  proportionate
adjustment  in the event of a stock  split,  stock  dividend or other  change in
capitalization.  All interest accrued and unpaid as of any Interest Payment Date
shall be added to principal and accrue interest from such Interest Payment Date.

     1. Payments;  Voluntary Prepayment.  All payments of principal and interest
in respect of this Note  shall be made in lawful  money of the United  States of
America.  Each payment made  hereunder  shall be credited first to interest then
due and the  remainder  of such  payment  shall be  credited to  principal,  and
interest shall thereupon  cease to accrue upon the principal so credited.  Maker
shall have the right at any time and from time to time to prepay  the  principal
of this Note in whole or in part,  without  premium or penalty,  such prepayment
hereunder  being  accompanied  by interest on the  principal  amount of the Note
being  prepaid to the date of  prepayment.  All voluntary  prepayments  shall be
applied to the remaining principal payments in chronological order of maturity.

     2. Mandatory Prepayment.

     (a) If there shall occur a termination  for Cause or Voluntary  Termination
(as such terms are defined in the Program) of Maker, the unpaid principal amount
of this Note together with accrued interest thereon shall become due and payable
on the 60th business day after such termination.

     (b) If the  Program is not  approved by Payee's  stockholders  on or before
June 22, 2000,  the unpaid  principal of and all accrued and unpaid  interest on
this Note shall become immediately due and payable.

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     3. Full Recourse Note. This Note is a full recourse Note and Maker shall be
liable for the full payment of the principal of and interest on this Note.

     4. Events of Default.  Each of the following  shall  constitute an Event of
Default:

     (a) The  failure  by Maker to pay any  principal  under this Note when due,
whether at stated maturity, by acceleration, or otherwise, or the failure to pay
any  interest or other amount due under this Note within five (5) days after the
date due;

     (b) any challenge,  or institution of any proceedings to challenge by Maker
of  the  validity,  binding  effect  or  enforceability  of  this  Note  or  any
endorsement of this Note;

     (c) any default by Maker of any other obligation under this Note; or

     (d)  The  initiation  of  any  proceeding   relating  to  Maker  under  any
bankruptcy,  reorganization,  arrangement of debt,  insolvency,  readjustment of
debt or receivership  law or statute,  whether filed by or against Maker, or the
assignment for the benefit of creditors by Maker.

     Upon an Event of  Default  set  forth in  clauses  (a) and (d)  above,  the
principal  amount of this Note  together  with accrued  interest  thereon  shall
become immediately due and payable, without presentment, demand, notice, protest
or other  requirements of any kind (all of which are hereby  expressly waived by
Maker). Upon any other Event of Default,  Payee may, by written notice to Maker,
declare the principal amount of this Note together with accrued interest thereon
to be due and payable,  and the principal amount of this Note together with such
interest shall thereupon immediately become due and payable without presentment,
further  notice,  protest  or other  requirements  of any kind (all of which are
hereby expressly waived by Maker).

     5.  Set-Off.  Payee shall be entitled to set-off  against this Note any and
all  amounts  owed by Payee to Maker as and when  such  amounts  become  due and
payable, whether presently existing or hereafter incurred, to the maximum extent
allowable  under  applicable  laws.  To the extent that  Maker's  consent to the
set-off is required, this Note constitutes Maker's consent.

     6. Miscellaneous.

     (a) All notices and other communications provided for hereunder shall be in
writing  (including  facsimile  or  e-mail  communication)  and  hand-delivered,
mailed,  or telecopied as follows:  if to Maker,  at Maker's  address  specified
opposite Maker's  signature  below;  and if to Payee, at 2141 Rosecrans  Avenue,
Suite  4000,  CA  90245;  or in each  case at such  other  address  as  shall be
designated by Payee or Maker. All such notices and  communications  shall,  when
hand-delivered,   mailed,  or  telecopied  (with  answer-back  confirmation)  be
effective when deposited in the mails, delivered or sent by telecopier.

     (b) No  failure  or delay on the part of Payee or any other  holder of this
Note to exercise any right,  power or privilege under this Note and no course of
dealing  between Maker and Payee shall impair such right,  power or privilege or
operate as a waiver of any  default or an  acquiescence  therein,  nor shall any
single or partial  exercise of any such right,  power or privilege  preclude any
other or further exercise  thereof or the exercise of any other right,  power or
privilege.  The  rights  and  remedies  expressly  provided  in  this  Note  are
cumulative  to, and not  exclusive  of, any rights or remedies  that Payee would
otherwise  have. No notice to or demand on Maker in any case shall entitle Maker
to any other or further  notice or demand in similar or other  circumstances  or
constitute a waiver of the right of Payee to any other or further  action in any
circumstances without notice or demand.

     (c) Maker and any  endorser  of this Note hereby  consent to  renewals  and
extensions of time at or after the maturity hereof,  without notice,  and hereby
waive diligence,  presentment,  protest, demand and notice of every kind and, to
the full extent  permitted by law, the right to plead any statute of

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limitations  as a  defense  to  any  demand  hereunder.  To the  fullest  extent
permitted by law, the obligations of Maker hereunder shall not be subject to any
counterclaim,  set-off, deduction, diminution, abatement, recoupment, deferment,
suspension,  reduction or defense (other than the full and strict  compliance by
Maker with  those  obligations)  based on any claim that Maker may have  against
Payee or any other person.

     (d) No provision of this Note may be waived, modified or discharged orally,
but only by an agreement signed by the party against whom enforcement is sought.

     (e) If any  provision  in or  obligation  under this Note shall be invalid,
illegal  or  unenforceable  in any  jurisdiction,  the  validity,  legality  and
enforceability of the remaining provisions or obligations,  or of such provision
or  obligation  in any other  jurisdiction,  shall not in any way be affected or
impaired thereby.

     (f) This note and the rights and  obligations of maker and payee  hereunder
shall be governed by, and shall be construed and enforced in accordance with the
laws of the State of  California  except for such  matters as are subject to the
General Corporation Law of the State of Delaware.

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<PAGE>    4

     IN WITNESS  WHEREOF,  Maker has executed and delivered  this Note as of the
day and year and at the place first above written.


                                                        MAKER

                                                        CHARLES R. WILLIAMSON
                                                        ------------------------
                                                        Print Name

                                                        /s/CHARLES R. WILLIASON
                                                        ------------------------
                                                        Signature

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<PAGE>    5

                         TRANSACTIONS ON PROMISSORY NOTE


                                      Amount of                  Outstanding
         Amount of            Principal Repaid on this      Principal Balance on
         Loan Made                      Date                      this Date
Date    on this Date
----    ------------          ------------------------      --------------------


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