<PAGE>


                                                               Exhibit 4(B)-1(B)

                         TEXAS EASTERN TRANSMISSION, LP

                                       TO

                            THE CHASE MANHATTAN BANK

                                                Trustee


                              ___________________

                         Second Supplemental Indenture

                           Dated as of April 16, 2001

                              ___________________

                                to the Indenture

                          Dated as of December 1, 2000

                              ___________________
<PAGE>

                             TABLE OF CONTENTS (1)

                                                                    Page
                                                                    ----
                                   ARTICLE 1

                                   ASSUMPTION

SECTION 101.    Assumption..........................................  2
SECTION 102.    Succession and Substitution.........................  2
SECTION 103.    Representation......................................  2


                                   ARTICLE 2

                                 MISCELLANEOUS

SECTION 201.    Recitals............................................  2
SECTION 202.    Ratification and Incorporation of Original
                Indenture...........................................  2
SECTION 203.    Executed in Counterparts............................  2
SECTION 204.    Capitalized Terms not Defined.......................  2
-----------
(1)  This Table of Contents does not constitute part of the Indenture or have
     any bearing upon the interpretation of any of its terms and provisions.

                                       i
<PAGE>

     THIS SECOND SUPPLEMENTAL INDENTURE is made as of the 16th day of April,
2001, between TEXAS EASTERN TRANSMISSION, LP, a Delaware limited partnership
("TLP" or the "successor Company") having its principal office at 5400
Westheimer Court, Houston, Texas 77056, and THE CHASE MANHATTAN BANK, a New York
banking corporation, as Trustee (herein called the "Trustee").

                                  WITNESSETH:

     WHEREAS, Texas Eastern Transmission Corporation, a Delaware Corporation
(the "Company"), has heretofore entered into an Indenture, dated as of December
1, 2000 with The Chase Manhattan Bank, as Trustee, which Indenture was amended
by a First Supplemental Indenture, dated as of April 16, 2001 (the "Original
Indenture");

     WHEREAS, the Original Indenture is incorporated herein by this reference
and the Original Indenture, as amended by this Second Supplemental Indenture, is
herein called the "Indenture";

     WHEREAS, the Company has heretofore issued in accordance with the
provisions of the Original Indenture, and now has outstanding, its 7.30% Notes
due 2010 in the aggregate principal amount of $300,000,000;

     WHEREAS, as of the date hereof, the Company has converted into TLP in
accordance with Section 266 of the Delaware General Corporation Law and Section
17-217 of the Delaware Revised Uniform Limited Partnership Act;

     WHEREAS, the Original Indenture provides that a partnership may, by
conversion of the Company into such partnership, succeed to, and be substituted
for, the Company upon the satisfaction of certain conditions provided in the
Original Indenture;

     WHEREAS, TLP desires to evidence its succession to the Company under the
Indenture and to assume the covenants of the Company in the Indenture and the
Securities and be substituted for the Company thereunder;

     WHEREAS, this Second Supplemental Indenture may be entered into for the
aforementioned purpose without the consent of any Holders of Securities pursuant
to Sections 901(1) of the Original Indenture; and

     WHEREAS, all conditions necessary to authorize the execution and delivery
of this Second Supplemental Indenture and to make it a valid and binding
obligation of TLP have been done or performed.

     NOW, THEREFORE, in consideration of the agreements and obligations set
forth herein and for other good and valuable consideration, the sufficiency of
which is hereby acknowledged, the parties hereto hereby agree as follows:
<PAGE>

                                   ARTICLE 1

                                   ASSUMPTION

     SECTION 101. Assumption. TLP hereby expressly assumes the due and punctual
payment of the principal of and premium, if any, and interest on all of the
Securities, according to their tenor, and the due and punctual performance and
observance of all of the covenants and conditions of the Original Indenture to
be performed by the Company.

     SECTION 102. Succession and Substitution. The Trustee hereby acknowledges
that, as of the date hereof, TLP shall succeed to, and be substituted for, and
may exercise every right and power of, the Company under the Indenture with the
same effect as if TLP had been named as the Company therein and thereafter the
Company shall be relieved of all obligations and covenants under the Indenture
and the Securities.

     SECTION 103. Representation. TLP hereby represents that it is a partnership
organized and validly existing under the laws of the State of Delaware.


                                   ARTICLE 2

                                 MISCELLANEOUS

     SECTION 201. Recitals. The recitals in this Second Supplemental Indenture
are made by the successor Company only and not by the Trustee; the Trustee makes
no representation and shall have no responsibility for, and in respect of, the
validity or sufficiency of this Second Supplemental Indenture or the execution
hereof by the successor Company; and all of the provisions contained in the
Original Indenture in respect of the rights, privileges, immunities, powers and
duties of the Trustee shall be applicable in respect of this Second Supplemental
Indenture as fully and with like effect as if set forth herein in full.

     SECTION 202. Ratification and Incorporation of Original Indenture. As
supplemented hereby, the Original Indenture is in all respects ratified and
confirmed, and the Original Indenture and this Second Supplemental Indenture
shall be read, taken and construed as one and the same instrument.

     SECTION 203. Executed in Counterparts. This Second Supplemental Indenture
may be executed in several counterparts, each of which shall be deemed to be an
original, and such counterparts shall together constitute but one and the same
instrument.

     SECTION 204. Capitalized Terms not Defined. Any capitalized terms not
defined in this Second Supplemental Indenture shall have the definitions
provided in the Original Indenture.

                                       2
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this instrument to be
duly executed as of the day and year first above written.

                               TEXAS EASTERN TRANSMISSION, LP


                               By:  Duke Energy Gas Transmission Services, LLC,
                                       its General Partner



                                   By:  /s/ Alan N. Harris
                                       -----------------------------------
                                        Vice President, Controller and Treasurer
Attest:

 /s/ Beverly J. Fite
--------------------------
 Assistant Secretary

                               THE CHASE MANHATTAN BANK,
                                 as Trustee



                               By: /s/ J.D. Heaney
                                  ------------------------------------------
                                   J.D. Heaney
                                   Vice President

Attest:

 /s/ Diane Darconte
--------------------------

                                       3