<PAGE>

                                                                     EXHIBIT 4.1


                                  GLOBAL NOTE

UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), NEW YORK, NEW YORK, TO
THE COMPANY OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND
ANY CERTIFICATE 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.

TRANSFERS OF THIS GLOBAL SECURITY SHALL BE LIMITED TO TRANSFERS IN WHOLE, BUT
NOT IN PART, TO NOMINEES OF DTC OR TO A SUCCESSOR THEREOF OR SUCH SUCCESSOR'S
NOMINEE AND TRANSFERS OF PORTIONS OF THIS GLOBAL SECURITY SHALL BE LIMITED TO
TRANSFERS MADE IN ACCORDANCE WITH THE RESTRICTIONS SET FORTH IN THE INDENTURE
REFERRED TO HEREIN.

R-GN1                                                        Principal Amount

                      ENTERPRISE PRODUCTS OPERATING L.P.     $450,000,000

                          7.50% SENIOR NOTE DUE 2011

                                                               CUSIP 293791 AB 5

ENTERPRISE PRODUCTS OPERATING L.P., a limited partnership duly organized and
existing under the laws of the State of Delaware (herein called the "Company",
which term includes any successor corporation or other entity under the
Indenture referred to below), for value received, hereby promises to pay to Cede
& Co., as the nominee of DTC, or registered assigns, the principal amount of
Four Hundred Fifty Million Dollars ($450,000,000), on February 1, 2011 (the
"Maturity Date") and to pay interest (computed on the basis of a 360-day year of
twelve 30-day months) on February 1 and August 1 ("Interest Payment Date") of
each year, beginning on August 1, 2001, and at the Maturity Date specified above
on said principal amount, at the rate of 7.50% per annum, from the date hereof
until payment of said principal amount has been made or duly provided for. The
interest so payable on any Interest Payment Date (other than at maturity) will
be paid to the Person in whose name this Global Note is registered at the close
of business on the fifteenth day of the month immediately preceding the month in
which such interest payment is due (a "Regular Record Date"), unless the Company
shall default in the payment of interest due on any such Interest Payment Date,
in which case such defaulted interest shall be paid to the Person in whose name
this Global Note is registered at the close of business on a special record date
for the payment of such defaulted interest established by notice to the
registered holders of Notes not less than ten (10) days preceding such special
record date. In any case, where the date for any
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payment on the Notes is not a Business Day, such payment shall be made on the
next succeeding Business Day.

Both principal of, premium, if any, and interest on this Global Note are payable
in immediately available funds in any coin or currency of the United States of
America which at the time of payment is legal tender for the payment of public
and private debts.  Payments of principal of, premium, if any, and interest will
be made by wire transfer of immediately available funds to the Depositary or its
nominee, in its capacity as registered holder of this Global Note.  Initially,
the Trustee will act as paying agent and registrar under the Indenture.  The
Company may change any paying agent or registrar as provided in the Indenture.

This Global Note is one of a duly authorized issue of debentures, notes, bonds
or other evidences of indebtedness of the Company (the "Securities"), of the
series hereinafter specified, issued or to be issued under an Indenture dated as
of March 15, 2000, duly executed and delivered by the Company and Enterprise
Products Partners L.P., as Guarantor, to First Union National Bank, a banking
corporation existing under the laws of the United States of America, as trustee
(the "Trustee"), to which Indenture reference is hereby made for a description
of the respective rights and duties thereunder of the Trustee, the  Company, the
Guarantor and the Holders of the Securities.  The Securities may be issued in
one or more series, which different series may be issued in various aggregate
principal amounts, may mature at different times, may bear interest at different
rates, may be subject to different redemption provisions, may be subject to
different sinking, purchase or analogous funds, may be subject to different
covenants and events of default and may otherwise vary as in the Indenture
provided.  This Global Note is a Global Security representing the entire
principal amount of a series of Securities designated "7.50% Senior Notes Due
2011" (the "Notes") issued under the Indenture. Unless otherwise provided
herein, all terms used in this Global Note that are defined in the Indenture
shall have the meanings assigned to them in the Indenture.  The terms of the
Notes include those stated in the Indenture and those made part of the Indenture
by reference to the Trust Indenture Act of 1939.  To the extent permitted by
applicable law, in the event of any inconsistency between the terms of the Notes
and the terms of the Indenture, the terms of the Indenture shall govern.

The Notes are general, unsecured, senior obligations of the Company, and are
unconditionally guaranteed by the Guarantor as set forth in Article XIV of the
Indenture, as noted in the Notation of Guarantee to this Global Note.

The Notes shall not be redeemable through the operation of any sinking fund or
analogous provisions, nor at the option of a Holder.

The Notes will be redeemable, at the Company's option, at any time in whole, or
from time to time in part, upon not less than 30 and not more than 60 days
notice, at a price equal to the greater of (i) 100% of the principal amount of
the Notes to be redeemed or (ii) the sum of the present value of the remaining
scheduled payments of principal and interest (at the rate in effect on the date
of calculation of the redemption price) thereon (exclusive of interest accrued
to the date of redemption) discounted to the date of redemption on a semi-annual
basis (assuming a 360-day year consisting of twelve 30-day months) at the
applicable Treasury Yield plus 30 basis points, plus, in either case, accrued
interest to the date of redemption.

                                       2
<PAGE>

For purposes of determining the optional redemption price, the following
definitions are applicable:

     "Treasury Yield" means, with respect to any Redemption Date applicable to
     the Notes, the rate per annum equal to the semi-annual equivalent yield to
     maturity (computed as of the third business day immediately preceding such
     Redemption Date) of the Comparable Treasury Issue, assuming a price for the
     Comparable Treasury Issue (expressed as a percentage of its principal
     amount) equal to the applicable Comparable Treasury Price for such
     Redemption Date.

     "Comparable Treasury Issue" means the United States Treasury security
     selected by an Independent Investment Banker as having a maturity
     comparable to the remaining term of the Notes 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 terms of the Notes.

     "Independent Investment Banker" means Goldman, Sachs & Co. and Salomon
     Smith Barney Inc. (and their successors), or, if such firm is unwilling or
     unable to select the applicable Comparable Treasury Issue, an independent
     investment banking institution of national standing appointed by the
     Trustee and reasonably acceptable to the Company.

     "Comparable Treasury Price" means, with respect to any Redemption Date, (a)
     the bid price for the Comparable Treasury Issue (expressed as a percentage
     of its principal amount) at 4:00 P.M. on the third business day preceding
     such Redemption Date, as set forth on "Telerate Page 500" (or such other
     page as may replace Telerate Page 500), or (b) if such page (or any
     successor page) is not displayed or does not contain such bid prices at
     such time (i) the average of the Reference Treasury Dealer Quotations
     obtained by the Trustee for such Redemption Date, after excluding the
     highest and lowest of four such Reference Treasury Dealer Quotations, or
     (ii) if the Trustee is unable to obtain at least four such Reference
     Treasury Dealer Quotations, the average of all Reference Treasury Dealer
     Quotations obtained by the Trustee.

     "Reference Treasury Dealer" means Goldman, Sachs & Co. and Salomon Smith
     Barney Inc. (and their successors) and one other primary U.S. government
     securities dealer in New York City selected by each of the Independent
     Investment Bankers (each, a "Primary Treasury Dealer"); provided, however,
     that if any of the foregoing shall cease to be a Primary Treasury Dealer,
     the Company shall substitute therefor another Primary Treasury Dealer.

     "Reference Treasury Dealer Quotations" means, with respect to each
     Reference Treasury Dealer and any Redemption Date for the Notes, an
     average, as determined by the Trustee, of the bid and asked prices for the
     Comparable

                                       3
<PAGE>

     Treasury Issue for the Notes (expressed in each case as a percentage of its
     principal amount) quoted in writing to the Trustee by such Reference
     Treasury Dealer at 5:00 p.m., New York City time, on the third business day
     preceding such Redemption Date.

Holders of Notes to be redeemed will receive notice thereof by mail at least 30
and not more than 60 days prior to the date fixed for redemption.

In case an Event of Default with respect to the Notes shall have occurred and be
continuing, the principal of and interest on the Notes may be declared, and upon
such declaration shall become, immediately due and payable, in the manner, with
the effect and subject to the conditions provided in  the Indenture.  The
Indenture provides that such declaration may in certain events be waived by the
Holders of a majority in aggregate principal amount of the Notes then
Outstanding.

The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company or the Guarantor and the rights of the Holders of the Securities of each
series to be affected under the Indenture at any time by the Company, the
Guarantor and the Trustee with the consent of the Holders of not less than a
majority in aggregate principal amount of the Outstanding Securities of each
series to be affected.  It is also provided in the Indenture that the Holders of
a majority in aggregate principal amount of the Securities of such series at the
time Outstanding may on behalf of the Holders of all of the Securities of such
series waive any past default with respect to the Securities of such series
under the Indenture and rescind an acceleration and its consequences, except a
default in the payment of the principal of, premium, if any, and interest on,
any of the Securities of such series and a default in respect of any provision
of the Indenture that cannot be waived without the consent of each Holder
affected thereby.

The Indenture provides that no Holder of any Note may enforce any remedy under
the Indenture except in the case of neglect of the Trustee to act after notice
of default and after request by the Holders of not less than 25% in aggregate
principal amount of the Outstanding Notes and the offer to the Trustee of
reasonable indemnity satisfactory to it; provided, however, that such provision
shall not prevent the Holder hereof from enforcing payment of the principal of,
premium, if any, and interest on, this Global Note.

No reference herein to the Indenture and no provision of this Global Note or of
the Indenture (including the Company's right to defease and discharge the Notes
pursuant to Article XI of the Indenture) shall alter or impair the obligation of
the Company, which is absolute and unconditional, to pay the principal of,
premium, if any, and interest on, this Global Note at the place, at the
respective times, at the rate and in the coin or currency herein prescribed.

The Global Note shall be exchangeable for Securities registered in the names of
Persons other than the Depositary or its nominee only if (i) the Depositary
notifies the Company that it is unwilling or unable to continue as the
Depositary or if at any time the Depositary ceases to be eligible or in good
standing as a clearing agency registered under the United States Securities
Exchange Act of 1934, as amended, or other applicable statute, rule or
regulation and the

                                       4
<PAGE>

Company fails to appoint a successor Depositary within 90 days after the Company
receives such notice or becomes aware of such event, or (ii) the Company at any
time and in its sole discretion executes and delivers to the Trustee a Company
Order that this Global Note shall be so exchangeable. To the extent that this
Global Note is exchangeable pursuant to the preceding sentence, it shall be
exchangeable for Notes registered in such names as the Depositary shall direct.

Except as provided in the immediately preceding paragraph, this Global Note may
not be transferred except as a whole by the Depositary to a nominee of such
Depositary or by a nominee of such Depositary to such Depositary or another
nominee of such Depositary or by such Depositary or any such nominee to a
successor of such Depositary or a nominee of such successor.

Prior to due presentment for registration of transfer of this Global Note, the
Company, the Trustee and any agent of the Company or the Trustee may deem and
treat the Holder hereof as the absolute owner of this Global Note (whether or
not this Global Note shall be overdue and notwithstanding any notation of
ownership or other writing hereon), for the purpose of receiving payment hereof
or on account hereof, as herein provided, and for all other purposes, and
neither the Company, the Guarantor nor the Trustee nor any paying agent nor any
Registrar shall be affected by any notice to the contrary.  All payments made to
or upon the order of such Holder shall, to the extent of the sum or sums paid,
effectually satisfy and discharge liability for moneys payable on this Global
Note.

None of the Company, the Guarantor, the Trustee, any paying agent or any
Registrar will have any responsibility or liability for any aspect of the
records relating to or payments made on account of beneficial ownership
interests of this Global Note or for maintaining, supervising or reviewing any
records relating to such beneficial ownership interests.

The General Partner and its directors, officers, employees and members, as such,
shall have no liability for any obligations of the Guarantor or the Issuer under
the Notes, the Indenture or the Guarantee or for any claim based on, in respect
of, or by reason of, such obligations or their creation.  Each Holder by
accepting the Notes waives and releases all such liability.  The waiver and
release are part of the consideration for issuance of the Notes.

Except as otherwise expressly provided in this Global Note, this Global Note
shall in all respects be entitled to all benefits, and subject to the same terms
and conditions, as definitive registered securities authenticated and delivered
under the Indenture.

THE INDENTURE, THE GUARANTEE AND THIS GLOBAL NOTE SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

This Global Note shall not be valid or become obligatory for any purpose until
the certificate of authentication hereon shall have been signed by the Trustee
under the Indenture.

                                       5
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed by its sole General Partner.

Dated as of January 29, 2001            ENTERPRISE PRODUCTS OPERATING L.P.


                                        By:  Enterprise Products GP, LLC,
                                             as General Partner


                                        By:
                                           ---------------------------------
                                           Michael A. Creel
                                           Senior Vice President
                                           and Chief Financial Officer



TRUSTEE'S CERTIFICATE
OF AUTHENTICATION

This is one of the Securities of the
series designated herein referred
to in the within-mentioned
Indenture.

FIRST UNION NATIONAL BANK,
As Trustee


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

                                       6
<PAGE>

                                ASSIGNMENT FORM

     To assign this Note, fill in the form below: (I) or (we) for value
received, assign and transfer this Note to


-------------------------------------------------------------------------------
                 (Insert assignee's soc. sec. or tax I.D. no.)

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

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

-------------------------------------------------------------------------------
             (Print or type assignee's name, address and zip code)

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


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

Date: ________________________

                                     Your Signature:___________________________
                                     (Sign exactly as your name appears on the
                                     face of this Note)

                                     Signature Guarantee:

                                       7
<PAGE>

                  SCHEDULE OF EXCHANGES OF DEFINITIVE SECURITY

The following exchanges of a part of this Global Security for Definitive
Securities have been made:

<TABLE>
<CAPTION>
              Amount of decrease      Amount of increase       Principal Amount of         Signature of
              in Principal Amount     in Principal Amount     this Global Security      authorized officer
 Date of        of this Global          of this Global           following such            of Trustee or
 Exchange          Security                Security          decrease (or increase)     Security custodian
<S>             <C>                     <C>                     <C>                     <C>
</TABLE>

                                       8
<PAGE>

                             NOTATION OF GUARANTEE

     The Guarantor (which term includes any successor person under the
Indenture), has fully, unconditionally and absolutely guaranteed, to the extent
set forth in the Indenture and subject to the provisions in the Indenture, the
due and punctual payment of the principal of, and premium, if any, and interest
on the Notes and all other amounts due and payable under the Indenture and the
Notes by the Company.

     The obligations of the Guarantor to the Holders of Notes and to the Trustee
pursuant to the Guarantee and the Indenture are expressly set forth in Article
XIV of the Indenture and reference is hereby made to the Indenture for the
precise terms of the Guarantee.

                             ENTERPRISE PRODUCTS PARTNERS L.P.

                             By:  Enterprise Products GP, LLC
                                  Its General Partner


                             By:
                                --------------------------------------
                                 Michael A. Creel
                                 Senior Vice President
                                 and Chief Financial Officer

                                       9