<PAGE>   1


                                                                     Exhibit 4.4

                             COSTILLA ENERGY, INC.


No.
                                                             CUSIP No. 22161GAB9


         THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF
         1933, AS AMENDED (THE "SECURITIES ACT"), AND, ACCORDINGLY, MAY NOT BE
         OFFERED OR SOLD WITHIN THE UNITED STATES OR TO, OR FOR THE ACCOUNT OR
         BENEFIT OF, U.S. PERSONS EXCEPT AS SET FORTH BELOW.  BY ITS
         ACQUISITION HEREOF, THE HOLDER (1) REPRESENTS THAT (A) IT IS A
         "QUALIFIED INSTITUTIONAL BUYER" (AS DEFINED IN RULE 144A UNDER THE
         SECURITIES ACT) OR (B) IT IS AN "ACCREDITED INVESTOR" (AS DEFINED IN
         RULE 501(a)(1), (2), (3), OR (7) UNDER THE SECURITIES ACT) (AN
         "ACCREDITED INVESTOR"), OR (C) IT IS NOT A U.S. PERSON AND IS
         ACQUIRING THIS SECURITY IN AN OFFSHORE TRANSACTION IN COMPLIANCE WITH
         RULE 904 UNDER THE SECURITIES ACT, (2) AGREES THAT IT WILL NOT PRIOR
         TO THE DATE THAT IS TWO YEARS AFTER THE LATER OF THE ORIGINAL ISSUE
         DATE AND THE LAST DATE ON WHICH THE COMPANY OR ANY AFFILIATED PERSON
         OF THE COMPANY WAS THE OWNER OF THIS SECURITY RESELL OR OTHERWISE
         TRANSFER THIS SECURITY EXCEPT (A) TO THE COMPANY OR ANY SUBSIDIARY
         THEREOF, (B) INSIDE THE UNITED STATES TO A QUALIFIED INSTITUTIONAL
         BUYER IN COMPLIANCE WITH RULE 144A UNDER THE SECURITIES ACT, (C)
         INSIDE THE UNITED STATES TO AN ACCREDITED INVESTOR THAT, PRIOR TO SUCH
         TRANSFER, FURNISHES (OR HAS FURNISHED ON ITS BEHALF BY A U.S.
         BROKER-DEALER) TO THE TRUSTEE A SIGNED LETTER CONTAINING CERTAIN
         REPRESENTATIONS AND AGREEMENTS RELATING TO THE RESTRICTIONS ON
         TRANSFER OF THIS SECURITY (THE FORM OF WHICH LETTER CAN BE OBTAINED
         FROM THE TRUSTEE FOR THIS SECURITY), (D) OUTSIDE THE UNITED STATES IN
         AN OFFSHORE TRANSACTION IN COMPLIANCE WITH RULE 904 UNDER THE
         SECURITIES ACT, (E) PURSUANT TO THE EXEMPTION FROM REGISTRATION
         PROVIDED BY RULE 144 UNDER THE SECURITIES ACT (IF AVAILABLE), OR (F)
         PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES
         ACT AND (3) AGREES THAT IT WILL GIVE TO EACH PERSON TO WHOM THIS
         SECURITY IS TRANSFERRED A NOTICE SUBSTANTIALLY TO THE EFFECT OF THIS
         LEGEND.  IN CONNECTION WITH ANY TRANSFER OF THIS SECURITY PRIOR TO THE
         DATE THAT IS TWO YEARS AFTER THE LATER OF THE ORIGINAL ISSUE DATE AND
         THE LAST DATE ON WHICH THE COMPANY OR ANY AFFILIATED PERSON OF THE
         COMPANY WAS THE OWNER OF THIS
<PAGE>   2
         SECURITY, IF THE PROPOSED TRANSFEREE IS AN ACCREDITED INVESTOR, THE
         HOLDER MUST, PRIOR TO SUCH TRANSFER, FURNISH TO THE TRUSTEE AND THE
         COMPANY SUCH CERTIFICATIONS, LEGAL OPINIONS OR OTHER INFORMATION AS
         EITHER OF THEM MAY REASONABLY REQUIRE TO CONFIRM THAT SUCH TRANSFER IS
         BEING MADE PURSUANT TO AN EXEMPTION FROM, OR IN A TRANSACTION NOT
         SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT.  AS
         USED HEREIN, THE TERMS "OFFSHORE TRANSACTION," "UNITED STATES" AND
         "U.S. PERSON" HAVE THE MEANING GIVEN TO THEM BY REGULATION S UNDER THE
         SECURITIES ACT.

         THIS NOTE IS A GLOBAL NOTE WITHIN THE MEANING OF THE INDENTURE
         HEREINAFTER REFERRED TO.

         UNLESS THIS NOTE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
         DEPOSITORY TRUST COMPANY TO COSTILLA ENERGY, INC. OR THE REGISTRAR FOR
         REGISTRATION OF TRANSFER OR EXCHANGE AND ANY NOTE ISSUED IS REGISTERED
         IN THE NAME OF CEDE & CO. OR SUCH OTHER ENTITY AS HAS BEEN REQUESTED
         BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY (AND
         ANY PAYMENT HEREON IS MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS
         HAS BEEN REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY
         TRUST COMPANY), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
         OTHERWISE BY OR TO ANY PERSON IS WRONGFUL SINCE THE REGISTERED OWNER
         HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

         TRANSFER OF THIS GLOBAL NOTE SHALL BE LIMITED TO TRANSFERS IN WHOLE,
         AND NOT IN PART, TO NOMINEES OF THE DEPOSITORY TRUST COMPANY OR TO A
         SUCCESSOR THEREOF OR SUCH SUCCESSOR'S NOMINEE AND TRANSFERS OF
         INTERESTS IN THIS GLOBAL NOTE SHALL BE LIMITED TO TRANSFERS MADE IN
         ACCORDANCE WITH THE RESTRICTIONS SET FORTH IN SECTION 2.06 OF THE
         INDENTURE, DATED AS OF OCTOBER 1, 1996, AS AMENDED BY THE FIRST
         SUPPLEMENTAL INDENTURE DATED AS OF JANUARY 16, 1998, BETWEEN COSTILLA
         ENERGY, INC. AND THE TRUSTEE NAMED THEREIN, PURSUANT TO WHICH THIS
         NOTE WAS ISSUED.
<PAGE>   3
                                  GLOBAL NOTE
                   REPRESENTING 10 1/4% SENIOR NOTES DUE 2006


                 Costilla Energy, Inc., a Delaware corporation, for value
received, hereby promises to pay to CEDE & CO., or its registered assigns, the
principal sum indicated on Schedule A hereof, on October 1, 2006.

                 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 duly
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 purposes.

                 IN WITNESS WHEREOF, the Company has caused this Note to be
duly executed under its corporate seal.

                                        COSTILLA ENERGY, INC.


                                        By:

                                             Name:
                                             Title:

[Corporate Seal]

Attest:


By:
         Name:
         Title:

Dated:

TRUSTEE'S CERTIFICATE OF AUTHENTICATION

STATE STREET BANK AND TRUST COMPANY,
         as Trustee, certifies that this
         is one of the Notes referred to
         in the Indenture.


By:
         Authorized Signatory
<PAGE>   4
                          REVERSE SIDE OF GLOBAL NOTE


                             COSTILLA ENERGY, INC.

                                  GLOBAL NOTE
                   REPRESENTING 10 1/4% SENIOR NOTES DUE 2006


                 i.               Indenture.

                 This Note is one of a duly authorized issue of debt securities
of the Company (as defined below) designated as its "10 1/4% Senior Notes due
2006" (herein called the "Notes") limited in aggregate principal amount to
$80,000,000, issued under an indenture dated as of October 1, 1996, as amended
by the First Supplemental Indenture dated as of January 16, 1998 (as amended or
supplemented from time to time, the "Indenture") between the Company, certain
subsidiaries of the Company and State Street Bank and Trust Company, as trustee
(the "Trustee," which term includes any successor Trustee under the Indenture),
to which Indenture reference is hereby made for a statement of the respective
rights, limitations of rights, duties and immunities thereunder of the Company,
subsidiaries of the Company that have guaranteed the payment of the Notes (the
"Subsidiary Guarantors"), the Trustee and each Holder of Notes and of the terms
upon which the Notes are, and are to be, authenticated and delivered.  The
summary of the terms of this Note contained herein does not purport to be
complete and is qualified by reference to the Indenture.  All terms used in
this Note which are not defined herein shall have the meanings assigned to them
in the Indenture.

                 The Indenture restricts, among other things, the Company's and
its Subsidiaries' ability to incur additional indebtedness and issue preferred
stock, incur liens, pay dividends or make certain other restricted payments,
apply net proceeds from certain asset sales, enter into certain transactions
with affiliates, incur indebtedness, merge or consolidate with any other
person, sell stock of Subsidiaries or sell, assign, transfer, lease, convey or
otherwise dispose of substantially all of the assets of the Company.  The
Indenture permits, under certain circumstances, Subsidiaries of the Company to
be deemed Unrestricted Subsidiaries and thus not subject to the restrictions of
the Indenture.

                 ii.              Principal and Interest.

                 Costilla Energy, Inc., a Delaware corporation (such
corporation, and its successors and assigns under the Indenture hereinafter
referred to, being herein called the "Company"), promises to pay the principal
amount set forth on Schedule A of this Note to the Holder hereof on October 1,
2006.
<PAGE>   5
                 The Company shall pay interest on this Note at a rate of 10
1/4% per annum semiannually in arrears on April 1, and October 1, of each year,
commencing on April 1, 1998, to the Holder hereof until the principal amount
hereof is paid or duly provided for.  Interest shall accrue from the original
issue date or from the most recent Interest Payment Date thereafter to which
interest has been paid or duly provided for.  The interest so payable, and
punctually paid or duly provided for, on any Interest Payment Date will,
subject to certain exceptions provided in the Indenture, be paid to the Person
in whose name this Note (or the Note in exchange or substitution for which this
Note was issued) is registered at the close of business on the Record Date for
interest payable on such Interest Payment Date.  The Record Date for any
interest payment is the close of business on March 15, or September 15, as the
case may be, whether or not a Business Day, immediately preceding the Interest
Payment Date on which such interest is payable.  Any such interest not so
punctually paid or duly provided for ("Defaulted Interest") shall forthwith
cease to be payable to the Holder on such Record Date and shall be paid as
provided in Section 2.11 of the Indenture.  Interest will be computed on the
basis of a 360-day year of twelve 30-day months.

                 Each payment of interest in respect of an Interest Payment
Date will include interest accrued through the day before such Interest Payment
Date.  If an Interest Payment Date falls on a day that is not a Business Day,
the interest payment to be made on such Interest Payment Date will be made on
the next succeeding Business Day with the same force and effect as if made on
such Interest Payment Date, and no additional interest will accrue as a result
of such delayed payment.

                 To the extent lawful, the Company shall pay interest on
overdue principal, overdue premium, and Defaulted Interest (without regard to
any applicable grace period), at the interest rate borne on the Notes.  The
Company's obligation pursuant to the previous sentence shall apply whether such
overdue amount is due at its Stated Maturity, as a result of the Company's
obligations pursuant to Section 3.05, Section 4.07 or Section 4.08 of the
Indenture, or otherwise.

                 iii.             Method of Payment.

                 The Company, through the Paying Agent, shall pay interest on
this Note to the registered Holder of this Note, as provided above.  The Holder
must surrender this Note to a Paying Agent to collect principal payments.  The
Company will pay principal, premium, if any, and interest in money of the
United States of America that at the time of payment is legal tender for
payment of all debts public and private.  Principal, premium, if any, and
interest will be payable at the office of the Paying Agent but, at the option
of the Company, interest may be paid by check mailed to the registered Holders
at their registered addresses; provided that all payments with respect to Notes
the Holders of which have given wire transfer instructions to the Company will
be required to be made by wire transfer of immediately available funds to the
accounts specified by the Holders thereof.

                 iv.              Paying Agent and Registrar.
<PAGE>   6
0                 Initially, the Trustee will act as Paying Agent and Registrar
under the Indenture.  The Company may, upon written notice to the Trustee,
appoint and change any Paying Agent or Registrar.  The Company or any of its
subsidiaries may act as Paying Agent or Registrar.

                 v.               Optional Redemption.

                 The Notes may not be redeemed at the Company's option prior to
October 1, 2001.  Thereafter, the Notes will be subject to redemption at the
option of the Company, in whole or in part, upon not less than 30 calendar
days' nor more than 60 calendar days' notice, at the redemption prices
(expressed as percentages of principal amount) set forth below, plus accrued
and unpaid interest thereon (if any) to the applicable Redemption Date, if
redeemed during the twelve-month period beginning on October 1 of the years
indicated below:

<TABLE>
 
                 Year                                                        Percentage
                 ----                                                        ----------
                 <S>                                                         <C>
                 2001                                                        105.125%
                 2002                                                        103.417%
                 2003                                                        101.708%
                 2004 and thereafter                                         100.000%
</TABLE>

                 Notwithstanding the foregoing, at any time on or before
October 1, 1999, the Company may (but shall not have the obligation to) redeem
up to $30.0 million in aggregate principal amount of the Notes and Existing
Notes (as defined in the Indenture) at a redemption price of 110.25% of the
principal amount thereof, plus accrued and unpaid interest thereon to the
Redemption Date, with the net proceeds of an Equity Offering made by the
Company; provided that at least $150.0 million in aggregate principal amount of
Notes and Existing Notes remains outstanding immediately after the occurrence
of such redemption.

                 The Notes are not subject to any sinking fund.

                 vi.      Notice of Redemption.

                 At least 30 calendar days but not more than 60 calendar days
before a Redemption Date, the Company will send a notice of redemption,
first-class mail, postage prepaid, to Holders of Notes to be redeemed at the
addresses of such Holders as they appear in the Security Register.

                 If less than all of the Notes are to be redeemed at any time,
the Notes to be redeemed will be chosen by the Trustee in accordance with the
Indenture.  If any Note is redeemed subsequent to a Record Date with respect to
any Interest Payment Date specified above and on or prior to such Interest
Payment Date, then any accrued interest will be paid on such Interest Payment
Date to the Holder of the Note at the close of business on such Record Date.
If money in an amount sufficient to pay the Redemption Price of all Notes (or
portions thereof) to be redeemed on the Redemption Date is deposited with the
Paying Agent on or before the applicable
<PAGE>   7
Redemption Date and certain other conditions are satisfied, interest on the
Notes or portions thereof to be redeemed on the applicable Redemption Date will
cease to accrue.

                 vii.     Repurchase at the Option of Holders upon Change of
Control.

                 Upon the occurrence of a Change of Control, each Holder of
Notes shall have the right to require the Company to purchase such Holder's
Notes, in whole or in part, in a principal amount that is an integral multiple
of $1,000, pursuant to a Change of Control Offer, at a purchase price in cash
equal to 101% of the aggregate principal amount thereof plus accrued and unpaid
interest thereon to the Change of Control Payment Date.

                 Within 30 calendar days following any Change of Control, the
Company shall send, or cause to be sent, by first-class mail, postage prepaid,
a notice regarding the Change of Control Offer to each Holder of Notes.  The
Holder of this Note may elect to have this Note or a portion hereof in an
authorized denomination purchased by completing the form entitled "Option of
Holder to Elect Purchase" appearing below and tendering this Note pursuant to
the Change of Control Offer.  Unless the Company defaults in the payment of the
Change of Control Purchase Price with respect thereto, all Notes or portions
thereof accepted for payment pursuant to the Change of Control Offer will cease
to accrue interest from and after the Change of Control Payment Date.

                 viii.    Repurchase at the Option of Holders upon Asset Sale.

                 If at any time the Company or any Subsidiary engages in any
Asset Sale, the Company shall, within 30 calendar days of the date the amount
of Excess Proceeds exceeds $5.0 million, use the then-existing Excess Proceeds
to make an offer to purchase from all Holders, on a pro rata basis, Notes in an
aggregate principal amount equal to the maximum principal amount that may be
purchased out of the then-existing Excess Proceeds, at a purchase price in cash
in an amount equal to 100% of the principal amount thereof plus accrued and
unpaid interest thereon, if any, to the Asset Sale Payment Date.  Upon
completion of an Asset Sale Offer (including payment of the Asset Sale Purchase
Price for accepted Notes), any surplus Excess Proceeds that were the subject of
such offer shall cease to be Excess Proceeds, and the Company may then use such
amounts for general corporate purposes.

                 Within 30 calendar days of the date the amount of Excess
Proceeds exceeds $5.0 million, the Company shall send, or cause to be sent, by
first-class mail, postage prepaid, a notice regarding the Asset Sale Offer to
each Holder of Notes.  The Holder of this Note may elect to have this Note or a
portion hereof in an authorized denomination purchased by completing the form
entitled "Option of Holder to Elect Purchase" appearing below and tendering
this Note pursuant to the Asset Sale Offer.  Unless the Company defaults in the
payment of the Asset Sale Purchase Price with respect thereto, all Notes or
portions thereof selected for payment pursuant to the Asset Sale Offer will
cease to accrue interest from and after the Asset Sale Payment Date.
<PAGE>   8
                 ix.              The Global Note.

                 So long as this Global Note is registered in the name of the
Depositary or its nominee, members of, or participants in, the Depositary
("Agent Members") shall have no rights under the Indenture with respect to this
Global Note held on their behalf by the Depositary or the Trustee as its
custodian, and the Depositary may be treated by the Company, the Trustee and
any agent of the Company or the Trustee as the absolute owner of this Global
Note for all purposes.  Notwithstanding the foregoing, nothing herein shall (i)
prevent the Company, the Trustee or any agent of the Company or the Trustee,
from giving effect to any written certification, proxy or other authorization
furnished by the Depositary or (ii) impair, as between the Depositary and its
Agent Members, the operation of customary practices governing the exercise of
the rights of a Holder of Notes.

                 The Holder of this Global Note may grant proxies and otherwise
authorize any Person, including Agent Members and Persons that may hold
interests in this Global Note through Agent Members, to take any action which a
Holder of Notes is entitled to take under the Indenture or the Notes.

                 Whenever, as a result of optional redemption by the Company, a
Change of Control Offer, an Asset Sale Offer or an exchange for Certificated
Notes, this Global Note is redeemed, repurchased or exchanged in part, this
Global Note shall be surrendered by the Holder thereof to the Trustee who shall
cause an adjustment to be made to Schedule A hereof so that the principal
amount of this Global Note will be equal to the portion not redeemed,
repurchased or exchanged and shall thereafter return this Global Note to such
Holder; provided that this Global Note shall be in a principal amount of $1,000
or an integral multiple of $1,000.

                 x.               Transfer and Exchange.

                 The Holder of this Global Note shall, by acceptance of this
Global Note, agree that transfers of beneficial interests in this Global Note
may be effected only through a book entry system maintained by such Holder (or
its agent), and that ownership of a beneficial interest in the Notes
represented thereby shall be required to be reflected in book entry form.

                 Transfers of this Global Note shall be limited to transfers in
whole and not in part, to the Depositary, its successors, and their respective
nominees.  Interests of beneficial owners in this Global Note shall be
transferred in accordance with the rules and procedures of the Depositary (or
its successors).

                 This Global Note shall be exchanged by the Company for one or
more Certificated Notes if (a) the Depositary (i) has notified the Company that
it is Unwilling or unable to continue as, or ceases to be, a clearing agency
registered under Section 17A of the Exchange Act and (ii) a successor to the
Depositary registered as a clearing agency under Section 17A of the Exchange
Act is not able to be appointed by the Company within 90 calendar days or (b)
the Depositary is
<PAGE>   9
at any time unwilling or unable to continue as Depositary and a successor to
the Depositary is not able to be appointed by the Company within 90 calendar
days.  If an Event of Default occurs and is continuing, the Company shall, at
the request of the Holder hereof, exchange all or part of this Global Note for
one or more Certificated Notes; provided that the principal amount of each of
such Certificated Notes and this Global Note, after such exchange, shall be
$1,000 or an integral multiple thereof.  Whenever this Global Note is exchanged
as a whole for one or more Certificated Notes, it shall be surrendered by the
Holder to the Trustee for cancellation.  Whenever this Global Note is exchanged
in part for one or more Certificated Notes, it shall be surrendered by the
Holder to the Trustee and the Trustee shall make the appropriate notations
hereon pursuant to Section 2.05(c) of the Indenture.  All Certificated Notes
issued in exchange for this Global Note or any portion hereof shall be
registered in such names, and delivered, as the Depositary shall instruct the
Trustee.

                 The Holder of this Note shall have the right to obtain from
the Company the information specified in Section 4.16 of the Indenture.

                 xi.              Denominations.

                 The Notes are issuable only in registered form without coupons
in denominations of $1,000 and integral multiples thereof of principal amount.

                 xii.             Unclaimed Money.

                 If money for the payment of principal, premium, if any, or
interest remains unclaimed for two years, the Trustee or Paying Agent shall pay
the money back to the Company at its request unless an abandoned property law
designates another Person.  After any such payment, Holders entitled to the
money must look only to the Company and not to the Trustee for payment unless
such abandoned property law designates another Person.

                 xiii.            Discharge and Defeasance.

                 Subject to certain conditions, the Company at any time may
terminate some or all of its obligations under the Notes and the Indenture if
the Company irrevocably deposits with the Trustee money or U.S. Government
Obligations for the payment of principal, premium, if any, and interest on the
Notes to redemption or maturity, as the case may be.

                 xiv.             Amendment, Waiver.

                 Subject to certain exceptions set forth in the Indenture, (i)
the Indenture, the Subsidiary Guarantees or the Notes may be amended with the
written consent of the Holders of at least a majority in principal amount of
the outstanding Notes and (ii) any past Default and its consequences may be
waived with the written consent of the Holders of at least a majority in
principal amount of the outstanding Notes.  Subject to certain exceptions set
forth in the Indenture
<PAGE>   10
and the Subsidiary Guarantees, without the consent of any Holder of Notes, the
Company, the Subsidiary Guarantors and the Trustee may amend the Indenture, the
Subsidiary Guarantees or the Notes (i) to evidence the succession of another
Person to (A) the Company and the assumption by such successor of the covenants
of the Company under the Indenture and contained in the Notes or (B) a
Subsidiary Guarantor and the assumption by such successor of the covenants of
such Subsidiary Guarantor contained in its Subsidiary Guarantee; (ii) to add
additional covenants or to surrender rights and powers conferred on the Company
or any Subsidiary; (iii) to add any additional Events of Default; (iv) to
provide for uncertificated Notes in addition to or in place of Certificated
Notes; (v) to evidence and provide for the acceptance of appointment under the
Indenture of a successor Trustee; (vi) to secure the Notes or the Subsidiary
Guarantees; (vii) to cure any ambiguity in the Indenture or the Subsidiary
Guarantees, to correct or supplement any provision in the Indenture or the
Subsidiary Guarantees which may be inconsistent with any other provision
therein or to add any other provisions with respect to matters or questions
arising under the Indenture, provided that such actions shall not adversely
affect the interests of the Holders in any material respect; (viii) to comply
with the requirements of the Commission in order to effect or maintain the
qualification of the Indenture under the Trust Indenture Act; or (ix) to
release any Subsidiary Guarantor pursuant to the Indenture.

                 xv.              Defaults and Remedies.

                 If an Event of Default occurs and is continuing, the Trustee
or the Holders of at least 25% in principal amount of the Notes, subject to
certain limitations, may declare all the Notes to be immediately due and
payable.  Certain events of bankruptcy or insolvency are Events of Default and
shall result in the Notes being immediately due and payable upon the occurrence
of such Events of Default without any further act of the Trustee or any Holder.

                 Holders of Notes may not enforce the Indenture or the Notes
except as provided in the Indenture.  The Trustee may refuse to enforce the
Indenture or the Notes unless it receives reasonable indemnity or security.
Subject to certain limitations, Holders of a majority in principal amount of
the Notes may direct the Trustee in its exercise of any trust or power under
the Indenture.  The Holders of a majority in principal amount of the then
outstanding Notes, by written notice to the Trustee, may rescind any
declaration of acceleration and its consequences if the rescission would not
conflict with any judgment or decree, and if a Events of Default have been
cured or waived except nonpayment of principal, interest or premium that has
become due solely because of the acceleration.

                 xvi.              Subsidiary Guarantee.

                 Subject to the limitations set forth in the Indenture and the
Subsidiary Guarantees, the payment of principal of, premium, if any, and
interest on the Notes will be guaranteed by each Subsidiary Guarantor.
<PAGE>   11
                 xvii.             Individual Rights of Trustee.

                 Subject to certain limitations imposed by the Trust Indenture
Act, the Trustee or any Paying Agent or Registrar, in its individual or any
other capacity, may become the owner or pledgee of Notes and may otherwise deal
with the Company or its Affiliates with the same rights it would have if it
were not Trustee, Paying Agent or Registrar, as the case may be, under the
Indenture.

                 xviii.            No Recourse Against Certain Others.

                 No director, officer, employee, incorporator or stockholder of
the Company or any Subsidiary Guarantor, as such, shall have any liability for
any obligations of the Company or such Subsidiary Guarantor under the Notes,
the Subsidiary Guarantees or the Indenture or for any claim based on, in
respect of, or by reason of, such obligations or their creation, solely by
reason of its status as a director, officer, employee, incorporator or
stockholder of the Company or any Subsidiary Guarantor.  By accepting a Note,
each Holder waives and releases all such liability (but only such liability) as
part of the consideration for issuance of such Note to such Holder.

                 xix.             Governing Law.

                 THE INDENTURE AND THIS NOTE SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK APPLICABLE TO
AGREEMENTS MADE AND TO BE PERFORMED IN SAID STATE.

                 The Company will furnish to any Holder of Notes upon written
request and without charge to the Holder a copy of the Indenture which has in
it the text of this Note.  Requests may be made to:

                             Costilla Energy, Inc.
                             400 West Illinois, 10th Floor
                             Midland, Texas 79701
                             Attention:  Chief Financial Officer
<PAGE>   12
                                   SCHEDULE A

                          SCHEDULE OF PRINCIPAL AMOUNT


The initial principal amount at maturity of this Note shall be $79,480,000.
The following decreases/increase in the principal amount at maturity of this
Note have been made:

<TABLE>
<CAPTION>
                                                                 Total Principal
                                                                 Amount at                     Notation
                   Decrease in           Increase in             Maturity                      Made by
Date of            Principal             Principal               Following such                or on
Decrease/          Amount at             Amount at               Decrease/                     Behalf of
Increase           Maturity              Maturity                Increase                      Trustee  
---------          -----------           -----------             --------------                ---------
<S>                <C>                   <C>                     <C>                           <C>

---------          -----------           -----------             -------------                 ---------

---------          -----------           -----------             -------------                 ---------

---------          -----------           -----------             -------------                 ---------

---------          -----------           -----------             -------------                 ---------

---------          -----------           -----------             -------------                 ---------
</TABLE>
<PAGE>   13
                                   ASSIGNMENT

                    (To be executed by the registered Holder
                 if such Holder desires to transfer this Note)


FOR VALUE RECEIVED ____________________ hereby sells, assigns and transfers
unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
TAX IDENTIFYING NUMBER OF TRANSFEREE


  -------------------------------------------------------------------------
                (Please print name and address of transferee)


this Note, together with all right, title and interest herein, and does hereby
irrevocably constitute and appoint _____________________________ Attorney to
transfer this Note on the Security Register, with full power of substitution.



Dated:  
      ---------------------

---------------------------
Signature of Holder                               Signature Guaranteed by an 
                                                  institution member of the
                                                  Signature Guaranty Medallion 
                                                  Program:


NOTICE:            The signature to the foregoing Assignment must correspond to
                   the name as written upon the face of this Note in every
                   particular, without alteration or any change whatsoever.
<PAGE>   14
                       OPTION OF HOLDER TO ELECT PURCHASE
                             (check as appropriate)

[ ]      In connection with the Change of Control Offer made pursuant to
         Section 4.07 of the Indenture, the undersigned hereby elects to have

         [ ]     the entire principal amount

         [ ]     $_________________ ($1,000 in principal amount or an integral
                 multiple thereof) of this Note

         repurchased by the Company.  The undersigned hereby directs the
         Trustee or Paying Agent to pay it or __________________ an amount in
         cash equal to 101% of the principal amount indicated in the preceding
         sentence, plus accrued and unpaid interest thereon, if any, to the
         Change of Control Payment Date.

[ ]      In connection with the Asset Sale Offer made pursuant to Section 4.08
         of the Indenture, the undersigned hereby elects to have

         [ ]     the entire principal amount

         [ ]     $_________________ ($1,000 in principal amount or an integral
                 multiple thereof) of this Note

         repurchased by the Company.  The undersigned hereby directs the
         Trustee or Paying Agent to pay it or ______________________ an amount
         in cash equal to 100% of the principal amount indicated in the
         preceding sentence, plus accrued and unpaid interest thereon, if any,
         to the Asset Sale Payment Date.

Dated:



Signature of Holder                               Signature Guaranteed by an
                                                  institution member of the
                                                  Signature Guaranty Medallion
                                                  Program

NOTICE:  The signature to the foregoing must correspond to the name as written
         upon the face of this Note in every particular, without alteration or
         any change whatsoever.