<PAGE>

                                                                 EXHIBIT 4(a)(2)

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                           CLECO UTILITY GROUP INC.

              [Formerly Central Louisiana Electric Company, Inc.]

                                      TO

                             THE BANK OF NEW YORK

                     [Successor to Bankers Trust Company],
                                                       as Trustee

                                ______________


                         FIRST SUPPLEMENTAL INDENTURE

                         DATED AS OF DECEMBER 1, 2000

                                ______________



                    Amendment and Modification to Indenture
                          dated as of October 1, 1988


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<PAGE>

     FIRST SUPPLEMENTAL INDENTURE, dated as of December 1, 2000, between CLECO
UTILITY GROUP INC. [formerly Central Louisiana Electric Company, Inc.], a
Louisiana corporation (the "Company"), having its principal office at 2030
                            -------
Donahue Ferry Road, Pineville, Louisiana 71360-5226, and The Bank of New York,
[successor to Bankers Trust Company], a banking corporation duly organized and
existing under the laws of the State of New York, as Trustee (the "Trustee"),
                                                                   -------
having its principal Corporate Trust Office at 101 Barclay Street, Floor 21W,
New York, New York 10286.

                            RECITALS OF THE COMPANY

     The Company executed and delivered its Indenture dated as of October 1,
1988 to the Trustee (the "Indenture"), to provide for the issuance from time to
                          ---------
time of its unsecured debentures, notes or other evidences of indebtedness, in
the manner and subject to the conditions set forth in the Indenture.

     Terms used herein without definition that are defined in the Indenture
shall have the respective meanings given them in the Indenture.

     The Company deems it desirable to amend the Indenture in certain respects
to clarify that the Company is permitted to consolidate with, or sell, lease or
convey all or substantially all of its assets to, or merge with or into any
other limited liability company.

     Section 901(8) of the Indenture provides that without the consent of any
Holders of Securities or coupons, the Company, when authorized by a Board
Resolution, and the Trustee may enter into a supplemental indenture to, among
other things, cure any ambiguity, correct or supplement any provision therein
which may be defective, or make any other provisions with respect to matters or
questions arising under the Indenture which shall not be inconsistent with the
provisions of the Indenture and which shall not adversely affect the interest of
the Holders of Securities of any series or any related coupons in any material
respect.

     The Company has duly authorized the execution and delivery of this First
Supplemental Indenture.

     All things necessary to make this First Supplemental Indenture a valid
agreement of the Company have been done.

     NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

     For and in consideration of the premises, the sum of one Dollar duly paid
by the Company to the Trustee, the receipt of which is hereby acknowledged, it
is mutually covenanted and agreed, for the equal and proportionate benefit of
all the Holders of the Securities or of series thereof, as follows:
<PAGE>

                                  ARTICLE ONE

                   AMENDMENTS AND MODIFICATIONS TO INDENTURE

     Section 1. The definition of "Corporation" in Section 101 of the Indenture
is amended in its entirety to read as follows:

          "'Corporation' or 'corporation' includes corporations, associations,
          companies (including without limitation limited liability companies)
          and business trusts."

     Section 2. The definition of "Voting Stock" in Section 101 of the Indenture
is amended in its entirety to read as follows:

          "'Voting Stock' means stock of the class or classes, or other
          ownership interests howsoever evidenced, having general voting power
          under ordinary circumstances to elect at least a majority of the board
          of directors, managers or trustees of such corporation, provided that,
                                                                  --------
          for the purposes hereof, stock or another ownership interest which
          carries only the right to vote conditionally on the happening of an
          event shall not be considered Voting Stock whether or not such event
          shall have happened."

     Section 3. (A)  In furtherance of the foregoing, references in the
Indenture to the corporate nature of the Company's existence shall, upon and
after giving effect to a consolidation by the Company with, or sale, lease or
conveyance of all or substantially all of the Company's assets to, or merger of
the Company with or into, another company, as the case may be, be deemed to
refer to the successor company.

                (B)  The Indenture shall be deemed amended and modified to the
extent necessary to give effect to the foregoing. Except as amended and modified
hereby, the Indenture shall remain in full force and effect.


                                  ARTICLE TWO

                                 MISCELLANEOUS

     Section 1. As amended and modified by this First Supplemental Indenture,
the Indenture shall be read, taken and construed as one and the same instrument.

                                      -2-
<PAGE>

     Section 2.  The Trustee assumes no duties, responsibilities or liabilities
by reason of this First Supplemental Indenture, other than as set forth in the
Indenture, as fully as if said terms and conditions were herein set forth at
length.

     Section 3.  This First Supplemental Indenture may be executed in any number
of counterparts, each of which, when so executed and delivered, shall be an
original; but such counterparts shall together constitute one and the same
instrument.

     Section 4.  This First Supplemental Indenture 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 such state.

     Section 5.  The dating of this First Supplemental Indenture as of December
1, 2000, is intended as and for the convenient identification of the First
Supplemental Indenture and is not intended to indicate that this First
Supplemental Indenture was executed and delivered on said date, this First
Supplemental Indenture being executed and effective on the dates of the
respective acknowledgments hereto attached.

                                      -3-
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this First Supplemental
Indenture to be executed in its corporate name and its corporate seal to be
hereunto affixed and attested by its duly authorized officers, all as of the
date first above written.

                                    CLECO UTILITY GROUP INC.

[SEAL]
                                    By:  /s/ THOMAS J. HOWLIN
                                         -----------------------------------
                                         Name:  Thomas J. Howlin
                                         Title: Sr. Vice President
ATTEST:


/s/ MICHAEL P. PRUDHOMME
-----------------------------------
Name:  Michael P. Prudhomme
Title: Secretary

Signed, sealed, acknowledged and delivered
by CLECO UTILITY GROUP INC.,
in the presence of:


/s/ K. MICHAEL SAWRIE
-----------------------------------
Name:


/s/  [ILLEGIBLE]
-----------------------------------
Name:

                     [Signatures continued on next page.]

                                      -4-
<PAGE>

     IN WITNESS WHEREOF, the Trustee has caused this First Supplemental
Indenture to be executed in its corporate name and its corporate seal to be
hereunto affixed and attested by its duly authorized officers, all as of the
date first above written.


                                    THE BANK OF NEW YORK, as Trustee

[SEAL]
                                    By:  /s/ ROBERT A. MASSIMILLO
                                         ------------------------
                                         Name:  Robert A. Massimillo
                                         Title: Assistant Vice President
ATTEST:


/s/ MARYBETH LEWICKI
-----------------------------------
Name:  MaryBeth Lewicki
Title: Vice President

Signed, sealed, acknowledged and delivered
by THE BANK OF NEW YORK
in the presence of:


/s/ JOSEPH A. LLORET
-----------------------------------
Name:  Joseph A. Lloret


/s/ ADA L. LI
-----------------------------------
Name:  Ada L. Li

                                      -5-
<PAGE>

STATE OF LOUISIANA

PARISH OF RAPIDES


     BE IT KNOWN, that on this 11th day of December, 2000, before me, the
undersigned authority, duly commissioned, qualified and sworn within and for the
State and Parish aforesaid, personally came and appeared:

                    1.  Thomas J. Howlin

                    2.  Michael P. Prudhomme

to me known to be the identical persons who executed the above and foregoing
instrument, who declared and acknowledged to me, Notary, in the presence of the
undersigned competent witnesses, that they are respectively (1) the Senior Vice
President and (2) the Secretary of Cleco Utility Group Inc. (the "Company");
                                                                  -------
that the seal impressed beside their respective signatures on the foregoing
First Supplemental Indenture is the official seal of the Company; that the
aforesaid instrument was signed and sealed by them, on this date, on behalf of
the Company by authority of a resolution duly adopted by the Board of Directors
of the Company on October 27, 2000; and that the above named persons acknowledge
said instrument to be the free act and deed of the Company.

                                1.  /s/ THOMAS J. HOWLIN
                                    --------------------
                                    Name:  Thomas J. Howlin
                                    Title: Sr. Vice President


                                2.  /s/ MICHAEL P. PRUDHOMME
                                    ------------------------
                                    Name:  Michael P. Prudhomme
                                    Title: Secretary

WITNESSES:


/s/ K. MICHAEL SAWRIE
---------------------------------------


/s/ [ILLEGIBLE]
---------------------------------------

                            /s/ BEATRICE P. NEWCOMB
                            -----------------------------
                                 Notary Public

                                      -6-
<PAGE>

STATE OF NEW YORK

COUNTY OF NEW YORK

     BE IT KNOWN, that on this 12th day of December, 2000, before me, the
undersigned authority, duly commissioned, qualified and sworn within and for the
State and County aforesaid, personally came and appeared:

                          1.  Robert A. Massimillo

                          2.  MaryBeth Lewicki

to me known to be the identical persons who executed the above and foregoing
instrument, who declared and acknowledged to me, Notary, in the presence of the
undersigned competent witnesses, that they are respectively (1) the Assistant
Vice President and (2) the Vice President of The Bank of New York (the
"Trustee"); that the seal impressed beside their respective signatures on the
 -------
foregoing First Supplemental Indenture is the official seal of the Trustee; that
the aforesaid instrument was signed and sealed by them, on this date, on behalf
of the Trustee by authority of its By-laws; and that the above named persons
acknowledge said instrument to be the free act and deed of the Trustee.

1. /s/ ROBERT A. MASSIMILLO           Name:  Robert A. Massimillo
   ------------------------           Title: Assistant Vice President


1. /s/ MARYBETH LEWICKI               Name:  MaryBeth Lewicki
   ------------------------           Title: Vice President


WITNESSES:

/s/ JOSEPH A. LLORET
---------------------------

/s/ ADA L. LI
---------------------------


                            /s/ WILLIAM J. CASSELS
                            ----------------------
Notary Public