<PAGE>

                                                                     EXHIBIT 3.8


The following amendments to Article IV of the By-laws of Ultramar Diamond
Shamrock Corporation were adopted effective January 1, 2000:

     SECTION 1.  General.  The officers of the Corporation shall be chosen by
                 --------
the Board of Directors and shall be a President, a Secretary, and a Treasurer.
The Board of Directors, in its discretion, may also choose a Chairman of the
Board of Directors (who must be a director), Chairman Emeritus of the Board of
Directors, and one or more Vice Presidents (including, without limitation,
Assistant, Executive, Senior, and Group), Assistant Secretaries, Assistant
Treasurers, and other officers.  Any number of offices may be held by the same
person, unless otherwise prohibited by law, the Certificate of Incorporation, or
these By-laws.  The officers of the Corporation need not be stockholders of the
Corporation nor, except in the case of the Chairman of the Board of Directors,
need such officers be directors of the Corporation.

     SECTION 4.  Chairman of the Board of Directors; Chairman Emeritus.  The
                 ------------------------------------------------------
Chairman of the Board of Directors, if there be one, shall preside at all
meetings of the stockholders and of the Board of Directors.  He shall be the
Chief Executive Officer of the Corporation, and except where by law the
signature of the President is required, the Chairman of the Board of Directors
shall possess the same power as the President to sign all contracts,
certificates, and other instruments of the Corporation which may be authorized
by the Board of Directors.  During the absence or disability of the President,
the Chairman of the Board of Directors shall exercise all the powers and
discharge all the duties of the President.  The Chairman of the Board of
Directors shall also perform such other duties and may exercise such other
powers as from time to time may be assigned to him by these By-laws or by the
Board of Directors.  The Board of Directors may appoint one or more persons to
the position of Chairman Emeritus of the Board of Directors.  The position of
Chairman Emeritus shall be an honorary position.  The Chairman Emeritus shall
perform such duties as may be requested from time to time by the Board of
Directors or the Chairman of the Board of Directors.  The Chairman Emeritus
shall not be elected for a term, but will serve at the discretion of the Board
of Directors.

     SECTION 5.  President.  The President shall, subject to the control of the
                 ----------
Board of Directors and, if there be one, the Chairman of the Board of Directors,
have general supervision of the business of the Corporation and shall see that
all orders and resolutions of the Board of Directors are carried into effect.
He shall execute all bonds, mortgages, contracts, and other instruments of the
Corporation requiring a seal, under the seal of the Corporation, except where
required or permitted by law to be otherwise signed or executed and except that
the other officers of the Corporation may sign and execute documents when so
authorized by these By-laws, the Board of Directors, or the President.  In the
absence or disability of the Chairman of the Board of Directors, or if there be
none, the President shall preside at all meetings of the stockholders and the
Board of Directors.  If there be no Chairman of the Board of Directors, the
President shall be the Chief Executive Officer of the Corporation.  The
President shall also perform such other duties and may exercise such other
powers as from time to time may be assigned to him by these By-laws or by the
Board of Directors.
<PAGE>

     SECTION 6.  Vice Presidents.  At the request of the President or in his
                 ----------------
absence or in the event of his inability or refusal to act (and if there be no
Chairman of the Board of Directors), the Vice President or the Vice Presidents
if there is more than one (in the order designated by the Board of Directors)
shall perform the duties of the President, and when so acting, shall have all
the powers of and be subject to all the restrictions upon the President.  Each
Vice President shall perform such other duties and have such other powers as the
Board of Directors from time to time may prescribe.  If there be no Chairman of
the Board of Directors and no Vice President, the Board of Directors shall
designate the officer of the Corporation who, in the absence of the President or
in the event of the inability or refusal of the President to act, shall perform
all the powers of and be subject to all the restrictions upon the President.


b-law amndmt