SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549



                                    FORM 8-K

                             Current Report Pursuant
                          to Section 13 or 15(d) of the

                         Securities Exchange Act of 1934



    Date of report (Date of earliest event reported)        March 27, 2001
                                                        ------------------------



                               UNOCAL CORPORATION
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)



                                    Delaware

--------------------------------------------------------------------------------
                 (State or Other Jurisdiction of Incorporation)



    1-8483                                   95-3825062
--------------------------------------------------------------------------------
(Commission File Number)                (I.R.S. Employer Identification No.)



2141 Rosecrans Avenue, Suite 4000, El Segundo, California         90245
--------------------------------------------------------------------------------

(Address of Principal Executive Offices)                       (Zip Code)



                                 (310) 726-7600

--------------------------------------------------------------------------------
              (Registrant's Telephone Number, Including Area Code)


Item 5.  Other Events.
-----------------------


The Bylaws of Unocal Corporation,  as amended effective March 27, 2001, is filed
as an exhibit under Item 7(c) of this report.


Item 7.  Financial Statements and Exhibits.

         (c)  Exhibits

          3   Bylaws of Unocal Corporation, as amended effective March 27, 2001.

                                       -1-



Pursuant  to the  requirements  of the  Securities  Exchange  Act of  1934,  the
registrant  has duly  caused  this  report  to be  signed  on its  behalf by the
undersigned, thereunto duly authorized.

                                                UNOCAL CORPORATION
                                                (Registrant)





Date:  April 5, 2001                        By:  /s/ JOE D. CECIL
-------------------------                       -------------------------------
                                                Joe D. Cecil
                                                Vice President and Comptroller

                                       -2-



                                  EXHIBIT INDEX


3        Bylaws of Unocal Corporation, as amended effective March 27, 2001.

                                      -3-