<PAGE>   1
                                                                     EXHIBIT 4.1


              THIS NOTE IS A GLOBAL SECURITY WITHIN THE MEANING OF THE INDENTURE
HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF A DEPOSITORY OR A
NOMINEE OF A DEPOSITORY. THIS NOTE IS EXCHANGEABLE FOR NOTES REGISTERED IN THE
NAME OF A PERSON OTHER THAN THE DEPOSITORY OR ITS NOMINEE ONLY IN THE LIMITED
CIRCUMSTANCES DESCRIBED IN THE INDENTURE AND MAY NOT BE TRANSFERRED EXCEPT AS A
WHOLE BY THE DEPOSITORY TO A NOMINEE OF THE DEPOSITORY OR BY A NOMINEE OF THE
DEPOSITORY TO THE DEPOSITORY OR ANOTHER NOMINEE OF THE DEPOSITORY.

              UNLESS THIS NOTE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF
THE DEPOSITORY TRUST COMPANY ("DTC") (55 WATER STREET, NEW YORK, NEW YORK) TO
THE ISSUER OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT AND
ANY NOTE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR SUCH OTHER NAME AS IS
REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC AND ANY PAYMENT IS MADE TO CEDE
& CO., OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE
OF DTC, ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO
ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER HEREOF, CEDE & CO., HAS
AN INTEREST HEREIN. UNLESS AND UNTIL IT IS EXCHANGED IN WHOLE OR IN PART FOR THE
INDIVIDUAL NOTES REPRESENTED HEREBY, THIS GLOBAL NOTE MAY NOT BE TRANSFERRED
EXCEPT AS A WHOLE BY DTC TO A NOMINEE OF DTC OR BY A NOMINEE OF DTC TO DTC OR
ANOTHER NOMINEE OF DTC OR BY DTC OR ANY SUCH NOMINEE TO A SUCCESSOR OF DTC OR A
NOMINEE OF SUCH SUCCESSOR.



<PAGE>   2
                                                           Cusip No. 12201P AC 0


                      BURLINGTON RESOURCES FINANCE COMPANY
                                   6.40% NOTES
                               DUE AUGUST 15, 2011


<Table>
<Caption>
Rate of Interest                  Maturity Date              Original Issue Date
----------------                  -------------              -------------------
<S>                              <C>                           <C>
     6.40%                       August 15, 2011               August 24, 2001



No. 001                                                         $[        ]
</Table>

              Burlington Resources Finance Company, an unlimited liability
company organized and existing under the laws of Nova Scotia, Canada (herein
called the "Company"), for value received, hereby promises to pay to Cede & Co.
or registered assigns, the principal sum of $[ ] on the Maturity Date shown
above, and to pay interest thereon, at the annual rate of interest shown above,
from the Original Issue Date shown above or from the most recent Interest
Payment Date (as hereinafter defined) to which interest has been paid or duly
provided for, payable semiannually on February 15 and August 15 of each year and
at maturity (an "Interest Payment Date"), commencing on the first such date
after the Original Issue Date shown above. Interest will be computed on the
basis of a 360-day year of twelve 30-day months.

              The interest so payable, and punctually paid or duly provided for,
on any Interest Payment Date or within five days thereafter will, as provided in
the Indenture, be paid to the person in whose name this Note is registered at
the close of business on the Record Date for any such Interest Payment Date,
which shall be the February 1 or August 1 next preceding the applicable Interest
Payment Date (whether or not a Business Day). Any such interest not so
punctually paid or duly provided for, and any interest payable on such defaulted
interest (to the extent lawful), will forthwith cease to be payable to the
Holder on such Record Date and shall be paid to the person in whose name this
Note is registered at the close of business on a special record date for the
payment of such defaulted interest to be fixed by the Trustee, notice of which
shall be given to Holders of Notes not less than ten days prior to such special
record date. Payment of the principal of (and premium, if any) and interest on
this Note will be made at the office of the Trustee, in such coin or currency of
the United States of America as at the time of payment is legal tender for
payment of public and private debts; provided, however, that, at the option of
the Company, payment of any installment of interest may be made by check mailed
to the address of the person entitled thereto as such address shall appear in
the Securities Register or by wire transfer to an account maintained by the
person entitled thereto as specified in the Securities Register, provided that
such person shall have given the Trustee appropriate and timely written wire
instructions.
<PAGE>   3

              REFERENCE IS HEREBY MADE TO THE FURTHER PROVISIONS OF THIS NOTE
SET FORTH ON THE REVERSE HEREOF, WHICH FURTHER PROVISIONS SHALL FOR ALL PURPOSES
HAVE THE SAME EFFECT AS IF SET FORTH AT THIS PLACE.

              Unless the certificate of authentication hereon has been executed
by the Trustee referred to on the reverse hereof by manual signature, this Note
shall not be entitled to any benefit under the Indenture or be valid or
obligatory for any purpose.



<PAGE>   4
                  IN WITNESS WHEREOF, Burlington Resources Finance Company has
caused this instrument to be executed in its corporate name by the facsimile
signature of its duly authorized officers and has caused a facsimile of its
corporate seal to be affixed hereunto or imprinted hereon.


                                       BURLINGTON RESOURCES FINANCE COMPANY


                                       By:
                                          --------------------------------------
                                           Name:  Daniel D. Hawk
                                           Title: Vice President and Treasurer

ATTEST:


By:
   ----------------------------------
    Name:  Anne Vaughan
    Title: Assistant Secretary


DATED:



<PAGE>   5
                     TRUSTEE'S CERTIFICATE OF AUTHENTICATION


              This is one of the 6.40% Notes due August 15, 2011 issued pursuant
to the within-mentioned Indenture.

                                       CITIBANK, N.A.,
                                         as Trustee


                                       By:
                                          --------------------------------------
                                           Authorized Signatory
                                           Dated:





<PAGE>   6
                      BURLINGTON RESOURCES FINANCE COMPANY
                                   6.40% NOTES
                               DUE AUGUST 15, 2011


              This Note is one of a duly authorized issue of Notes of the
Company (which term includes any successor Person under the Indenture herein
referred to) designated as its 6.40% Notes due August 15, 2011 (the "Notes"),
issued or to be issued pursuant to an Indenture, dated as of February 12, 2001
(the "Indenture"), between the Company and Citibank N.A., as Trustee (the
"Trustee," which term includes any successor trustee under the Indenture). The
Notes shall be fully and unconditionally guaranteed by Burlington Resources
Inc., a Delaware corporation (the "Guarantor"), pursuant to a Guarantee
Agreement dated as of February 12, 2001 by the Guarantor in favor of the holders
of Notes. The terms of this Note include those stated in the Indenture and in
the Officers' Certificate issued thereunder and those made part of the Indenture
by reference to the Trust Indenture Act of 1939, as in effect on the date of the
Indenture. Reference is hereby made to the Indenture and the applicable
officers' certificate issued thereunder for a statement of the respective
rights, limitation of rights, duties and immunities thereunder of the Company,
the Trustee and the Holders and of the terms upon which the Notes are, and are
to be, authenticated and delivered.

              The Notes are a series of Securities issued or to be issued by the
Company under the Indenture, and this Series is unlimited in aggregate principal
amount. As of the Original Issue Date, $[ ] principal amount of Notes of this
Series will be issued. The Indenture provides that the Securities of the Company
referred to therein ("Securities"), may be issued in one or more Series, which
different Series may be issued in such aggregate principal amounts and on such
terms (including, but not limited to, terms relating to interest rate or rates,
provisions for determining such interest rate or rates and adjustments thereto,
maturity, redemption (optional and mandatory), covenants and Events of Default)
as may be provided in the officers' certificates or supplemental indentures
relating to the several Series.

              The Notes are subject to redemption upon not less than 30 nor more
than 60 days notice by mail, in whole or in part, at the option of the Company
at any time at a redemption price equal to the greater of (i) 100% of the
principal amount of such Notes plus accrued and unpaid interest to the
redemption date or (ii) the sum of the present values of the remaining scheduled
payments of principal and interest thereon (exclusive of interest accrued to the
date of redemption) discounted to the redemption date on a semiannual basis
(assuming a 360-day year consisting of twelve 30-day months) at the Treasury
Rate plus 25 basis points plus accrued and unpaid interest thereon to the
redemption date.

              "Treasury Rate" means, with respect to any redemption date, (i)
the yield, under the heading which represents the average for the immediately
preceding week, appearing in the most recently published statistical release
designated "H.15(519)" or any successor publication which is published weekly by
the Board of Governors of the Federal Reserve System and which establishes
yields on actively traded United States Treasury securities adjusted to constant
maturity under the caption "Treasury Constant Maturities," for the maturity
corresponding to the Comparable Treasury Issue (if no maturity is within three
months before or after the Remaining Life, yields for the two published

<PAGE>   7
                                       -2-


maturities most closely corresponding to the Comparable Treasury Issue shall be
determined and the Treasury Rate shall be interpolated or extrapolated from such
yields on a straight line basis, rounding to the nearest month) or (ii) if such
release (or any successor release) is not published during the week preceding
the calculation date or does not contain such yields, the rate per annum equal
to the semiannual equivalent yield to maturity of the Comparable Treasury Issue,
calculated using a price for the Comparable Treasury Issue (expressed as a
percentage of its principal amount) equal to the Comparable Treasury Price for
such redemption date. The Treasury Rate shall be calculated on the third
Business Day preceding the redemption date.

              "Business Day" means any calendar day that is not a Saturday,
Sunday or legal holiday in New York, New York and on which commercial banks are
open for business in New York, New York.

              "Comparable Treasury Issue" means the United States Treasury
security selected by an Independent Investment Banker as having a maturity
comparable to the remaining term ("Remaining Life") of the Notes to be redeemed
that would be utilized, at the time of selection and in accordance with
customary financial practice, in pricing new issues of corporate debt securities
of comparable maturity to the remaining term of the Notes.

              "Comparable Treasury Price" means, with respect to any redemption
date, (A) the average of four Reference Treasury Dealer Quotations for such
redemption date, after excluding the highest and lowest such Reference Treasury
Dealer Quotations, or (B) if the Independent Investment Banker obtains fewer
than four such Reference Treasury Dealer Quotations, the average of all such
Quotations.

              "Independent Investment Banker" means Salomon Smith Barney Inc. or
if such firm is unwilling or unable to select the Comparable Treasury Issue, an
independent investment banking institution of national standing appointed by the
Trustee.

              "Reference Treasury Dealer" means (i) each of Salomon Smith Barney
Inc. and three other primary U.S. Government securities dealers in New York City
(each, a "Primary Treasury Dealer") and their respective successors, provided,
however, that if any of the foregoing shall cease to be a Primary Treasury
Dealer, the Company will substitute therefor another Primary Treasury Dealer and
(ii) any other Primary Treasury Dealer selected by the Company.

              "Reference Treasury Dealer Quotations" means, with respect to each
Reference Treasury Dealer and any redemption date, the average, as determined by
the Independent Investment Banker, of the bid and asked prices for the
Comparable Treasury Issue (expressed in each case as a percentage of its
principal amount) quoted in writing to the Independent Investment Banker by such
Reference Treasury Dealer at 5:00 p.m. on the third Business Day preceding such
redemption date.

              If an Event of Default shall occur and be continuing, the
principal of all the Notes may be declared due and payable in the manner and
with the effect provided in the Indenture. The Indenture provides that the
Trustee or Holders of at least 25% in principal amount of the Securities of
<PAGE>   8
                                       -3-


the applicable series may declare the applicable series to be immediately due
and payable. However, upon certain conditions such declarations may be annulled
and past defaults may be waived.

              The Indenture permits, with certain exceptions as therein
provided, the amendment thereof and the modification of the rights and
obligations of the Company and the rights of the Holders of the Notes under the
Indenture at any time by the Company and the Trustee with the consent of the
Holders of a majority in aggregate principal amount of the Securities affected
thereby, voting as a single class (which may include the Notes), at the time
outstanding. The Indenture also contains provisions permitting the Company and
the Trustee to amend certain provisions of the Indenture without the consent of
the Holders of the Securities.

              No reference herein to the Indenture or the Officers' Certificate
and no provision of this Note or of the Indenture or the Officers' Certificate
shall alter or impair the obligation of the Company, which is absolute and
unconditional, to pay the principal of and interest on this Note at the times,
places and rates, and in the coin or currency, herein prescribed.

              As provided in the Indenture and subject to certain limitations
therein set forth, the transfer of this Note is registrable in the Securities
Register upon surrender of this Note for registration of transfer at the agency
of the Company provided for that purpose duly endorsed by, or accompanied by a
written instrument of transfer in substantially the form accompanying this Note
duly executed by, the Holder hereof or his attorney duly authorized in writing,
and thereupon one or more new Notes, of authorized denominations and for the
same aggregate principal amount, will be issued to the designated transferee or
transferees.

              The Notes are issuable only in registered form without coupons in
denominations of $1,000 and any integral multiple thereof. As provided in the
Indenture and subject to certain limitations set forth therein and on the face
of this Note, the Notes are exchangeable for a like aggregate principal amount
of Notes of a different authorized denomination, as requested by the Holder
surrendering the same.

              No service charge shall be made for any such registration of
transfer or exchange, but the Company may require payment of a sum sufficient to
cover any transfer tax or similar governmental charge payable in connection
therewith (other than any such transfer tax or similar governmental charge
payable upon exchanges pursuant to the Indenture in which case such transfer
taxes or similar governmental charges shall be paid by the Company).

              Prior to due presentment of this Note for registration of
transfer, the Company, the Trustee and any agent of the Company or the Trustee
may treat the person in whose name this Note is registered as the owner hereof
for all purposes, whether or not this Note be overdue, and neither the Company,
the Trustee nor any such agent shall be affected by notice to the contrary.

              All terms used in this Note which are defined in the Indenture or
the Officers' Certificate shall have the meanings assigned to them therein.



<PAGE>   9
                                       -4-


              Customary abbreviations may be used in the name of a Note holder
or any assignee, such as: TEN COM (= tenants in common), TEN ENT(= tenants by
the entireties), JT TEN (= joint tenants with right of survivorship and not as
tenants in common), CUST (= Custodian) and U/G/M/A (Uniform Gifts to Minors
Act).

              The Company will furnish to any Holder of record of a Note, upon
written request, without charge, a copy of the Indenture. Requests may be made
to: Vice President and Assistant Treasurer, Burlington Resources Finance
Company, c/o Burlington Resources Canada Energy Ltd., Suite 3700, 250-6th
Avenue, S.W., Calgary, Alberta T2P 3H7, telephone: (403) 260-8000.



<PAGE>   10
                                 ASSIGNMENT FORM


              If you the Holder want to assign this Note, fill in the form below
and have your signature guaranteed:

I or we assign and transfer this Note to:

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________
        (Print or type name, address and zip code and social security or
                          tax ID number of assignees)

and irrevocably appoint ________________________________________________________
agent to transfer this Note on the books of the Company. The agent may
substitute another to act for him.

Dated:                                    Signed:
      ---------------------------------          -------------------------------


                                                 -------------------------------
                                                  (Sign exactly as name appears
                                                  on the other side of the Note)

Signature Guarantee:
                    ------------------------------------------------------------

              NOTICE: Signature(s) must be guaranteed by a member firm of the
New York Stock Exchange or a commercial bank or trust company.




<PAGE>   11

                              [FORM OF GUARANTEE]

                                   GUARANTEE

              The undersigned Guarantor (capitalized terms used herein have the
meanings given such terms in the Indenture referred to in the Note upon which
this notation is endorsed) hereby unconditionally guarantees (such guarantee
being referred to herein as the "Guarantee") the due and punctual payment of the
principal of, premium, if any, and interest on the 6.40% Notes due August 15,
2011 (the "Notes") which this Guarantee accompanies, whether at maturity, by
acceleration or otherwise, the due and punctual payment of interest on the
overdue principal, premium and interest on the Notes, and the due and punctual
performance of all other obligations of the Company to the Holders or the
Trustee, all in accordance with the terms set forth in Article Two of the
Guarantee Agreement.

              This Guarantee shall not be valid or obligatory for any purpose
until the certificate of authentication on the Notes upon which this Guarantee
is noted shall have been executed by the Trustee under the Indenture by the
manual signature of one of its authorized officers.

              This Guarantee shall be governed by and construed in accordance
with the laws of the State of New York.

              This Guarantee is subject to release upon the terms set forth in
the Guarantee Agreement.

                                       BURLINGTON RESOURCES INC.


                                       By:
                                          --------------------------------------
                                           Name:
                                           Title: