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                                                                 Exhibit 10.9(b)


                           MILLENNIUM AMERICA HOLDINGS


                                  Amendment To

                       MILLENNIUM CHEMICALS GRANDFATHERED
                     SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN

                                  (the "Plan")


     The Plan shall be, and it hereby is, amended effective June 1, 2002 as
follows:

1.       Section 10.3 Change of Control

     Amend clause (iv) of Section 10.3 to read in its entirety as follows:


     "(iv) the stockholders of the Parent approve a plan of complete liquidation
     of the Parent or the closing of the sale or disposition by the Parent of
     all or substantially all of the Parent's assets other than the sale or
     disposition of all or substantially all of the assets of the Parent to one
     or more Subsidiaries (as defined below) of the Parent or to a person or
     persons who beneficially own, directly or indirectly, at least fifty
     percent (50%) or more of the combined voting power of the outstanding
     voting securities of the Parent at the time of the sale or disposition;
     provided, however, (y) the sale or disposition of all or any part of the
     Parent's interests in Equistar Chemicals, LP ("Equistar")(and all
     subsequent sales and dispositions of any securities or assets received as
     proceeds thereof, or as proceeds of proceeds) shall not be deemed to
     constitute a Change in Control, and (z) if the Parent sells or disposes
     of all or any part of the Parent's interests in Equistar indirectly (either
     through the sale or other disposition of any entity that owns, directly or
     indirectly, all or any part of the Parent's interests in Equistar, or
     otherwise), then the sale or disposition of the Parent's interests in
     Equistar (and all subsequent sales and dispositions of any securities or
     assets received as proceeds thereof, or as proceeds of proceeds) shall be
     ignored and disregarded in determining whether any such Change in Control
     has occurred. By way of illustration, if an indirect subsidiary of the
     Parent that owns the Parent's interests in Equistar together with certain
     other assets is sold, then, in determining whether a Change in Control has
     occurred, all relevant determinations shall be made pursuant to the
     assumption that (y) such subsidiary owns only such other assets, and (z)
     neither such subsidiary nor the Parent owns, either directly or indirectly,
     the interests in Equistar. "Subsidiary" shall have the meaning set forth in
     Section 424 of the Internal Revenue Code of 1986, as amended or superseded,
     and the term shall also include any partnership, limited liability company
     or other business entity if the Parent owns directly or indirectly,
     securities or other ownership interests representing at least fifty percent
     (50%) of the ordinary voting power or equity or capital interests of such
     entity."