AMENDMENT TO SHAREHOLDER RIGHTS AGREEMENT

     This FIRST AMENDMENT TO SHAREHOLDER RIGHTS AGREEMENT (this
"Amendment") is made and entered into as of March 29, 2006, by and between
Burlington Resources Inc., a Delaware corporation (the "Company"), and
Computershare Trust Company, N.A., a national banking association (the
"Rights Agent"). Except as otherwise provided herein, all capitalized terms
used herein shall have the meanings ascribed thereto in the Rights
Agreement.

                               R E C I T A L S

     WHEREAS, the Company and the Rights Agent are parties to that certain
Shareholder Rights Agreement dated as of December 16, 1998 (the "Rights
Agreement");

     WHEREAS, pursuant to Section 28 of the Rights Agreement, prior to the
Distribution Date, the Company and the Rights Agent shall, if the Company
so directs, amend any provision of the Rights Agreement without the
approval of any holders of certificates representing Common Stock; and

     WHEREAS, the Distribution Date has not yet occurred and subject to and
in accordance with the terms of this Amendment, the Company has directed
and the Rights Agent has agreed to amend the Rights Agreement in certain
respects, as more particularly set forth below.

                              A G R E E M E N T

     NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the undersigned hereby agree
to modify the Rights Agreement as set forth below.

     1. Amendment to Section 1(a). Section 1(a) of the Rights Agreement,
which sets forth the definition of "Acquiring Person," shall be amended by
adding the following paragraph at the end of Section 1(a):

     "Notwithstanding anything in this Agreement to the contrary, (i)
     neither Cello Acquisition Corp., a Delaware corporation ("Merger
     Sub"), nor any Affiliates or Associates of Merger Sub shall be deemed
     an Acquiring Person, (ii) no Distribution Date, Triggering Event or
     Stock Acquisition Date shall be deemed to occur and (iii) the Rights
     will not separate from the Common Stock, in each such case of clauses
     (i), (ii) and (iii), in connection with or as a result of the
     execution, delivery or performance of the Agreement and Plan of
     Merger, dated as of December 12, 2005, by and among ConocoPhillips, a
     Delaware corporation and parent of Merger Sub, Merger Sub and the
     Company (such agreement, including any amendment or supplement
     thereto, the "Merger Agreement"), or the consummation of the Merger or
     any of the transactions contemplated thereby. Capitalized terms used
     but not defined in this Agreement shall have the respective meanings
     set forth in the Merger Agreement. No such event shall entitle or
     permit the holders of the Rights to exercise the Rights or otherwise
     affect the rights of the holders of Rights, including giving the
     holders of the Rights the right to acquire securities of any party to
     the Merger Agreement."

     2. Amendment to Section 1(m). Section 1(m) of the Rights Agreement,
which sets forth the definition of "Section 11(a)(ii) Event" shall be
amended by adding the following sentence to the end of the section:

     "For avoidance of any doubt, notwithstanding anything in this
     Agreement to the contrary, a Section 11(a)(ii) Event shall not be
     deemed to have occurred in connection with or as a result of the
     execution, delivery or performance of the Merger Agreement, or the
     consummation of the Merger or any of the transactions contemplated
     thereby."

     3. Amendment to Section 1(n). Section 1(n) of the Rights Agreement,
which sets forth the definition of "Section 13 Event" shall be amended by
adding the following sentence to the end of the section:

     "For avoidance of any doubt, notwithstanding anything in this
     Agreement to the contrary, a Section 13 Event shall not be deemed to
     have occurred in connection with or as a result of the execution,
     delivery or performance of the Merger Agreement, or the consummation
     of the Merger or any of the transactions contemplated thereby."

     4. Amendment to Section 1(o). Section 1(o) of the Rights Agreement,
which sets forth the definition of "Stock Acquisition Date" shall be
amended by adding the following sentence to the end of the section:

     "For avoidance of any doubt, notwithstanding anything in this
     Agreement to the contrary, a Stock Acquisition Date shall not be
     deemed to have occurred in connection with or as a result of the
     execution, delivery or performance of the Merger Agreement, or the
     consummation of the Merger or any of the transactions contemplated
     thereby."

     5. Amendment to Section 1(q). Section 1(q) of the Rights Agreement,
which sets forth the definition of "Triggering Event" shall be amended by
adding the following sentence to the end of the section:

     "For avoidance of any doubt, notwithstanding anything in this
     Agreement to the contrary, a Triggering Event shall not be deemed to
     have occurred in connection with or as a result of the execution,
     delivery or performance of the Merger Agreement, or the consummation
     of the Merger or any of the transactions contemplated thereby."

     6. Amendment to Section 7(a)(i). Section 7(a)(i) of the Rights
Agreement shall be deleted in its entirety and replaced with the following:

     "the first to occur of (A) the moment immediately prior to the time at
     which the Merger becomes effective in accordance with the General
     Corporation Law of the State of Delaware or (B) the close of business
     on December 16, 2008 (the "Final Expiration Date"),"

     7. Confirmation of the Rights Agreement. Except as amended or modified
hereby, all terms, covenants and conditions of the Rights Agreement as
heretofore in effect shall remain in full force and effect and are hereby
ratified and confirmed in all respects.

     8. Governing Law. This Amendment shall be governed by and constituted
in accordance with the laws of the State of Delaware applicable to
contracts to be made and performed entirely within such State.

     9. Counterparts. This Amendment may be executed in any number of
counterparts, each of which when executed and delivered shall be deemed to
be an original and all such counterparts together, shall constitute one and
the same instrument.

     IN WITNESS WHEREOF, the parties hereto have executed this Amendment as
of the date first set forth above.

                                    BURLINGTON RESOURCES INC.


                                    By: /s/   L. David Hanower
                                        -----------------------
                                        Name: L. David Hanower
                                        Title:   Senior Vice President, Law
                                                 and Administration


                                    COMPUTERSHARE TRUST COMPANY, N.A.


                                    By: /s/  Katherine S. Anderson
                                        -----------------------------
                                        Name:  Katherine S. Anderson
                                        Title:    Managing Director