<PAGE>   1
                                                                    4(ii)(a)(6)

                                                                  EXECUTION COPY

                                 TRUST INDENTURE


        THIS TRUST INDENTURE (this "Indenture") dated as of this 25th day of
February, 1999 is entered into by and among GREAT RIVER CRUISE LINE, L.L.C., a
Delaware limited liability company ("Mortgagor"), and THE CHASE MANHATTAN BANK,
a New York banking corporation, as Agent (hereinafter in such capacity, the
"Agent"), as referred to and defined in the Credit Agreement described below,
THE FINANCIAL INSTITUTIONS LISTED ON THE SIGNATURE PAGES THEREOF of the Credit
Agreement described below and each other financial institution which from time
to time becomes a party thereto in accordance with Section 11.02(a) thereof
(together with their respective successors and permitted assigns, individually,
a "Lender" and, collectively, the "Lenders"), and THE CHASE MANHATTAN BANK, not
in its individual capacity but as trustee under this Indenture ("the Trustee").

                              PRELIMINARY STATEMENT

        A. The Agent, Hibernia National Bank, as Documentation Agent, the
Lenders and The Delta Queen Steamboat Co. (the "Borrower") have entered into a
Credit Agreement dated as of February 25, 1999 (as amended, restated,
supplemented or otherwise modified from time to time, the "Credit Agreement").
Capitalized terms used herein and not otherwise defined shall have the meanings
assigned thereto in the Credit Agreement; and

        B. In order to secure the Obligations (as defined in the Credit
Agreement ), the Mortgagor has executed and delivered a Preferred Ship Mortgage
dated February 25, 1999 (the "Mortgage") in favor of the Agent, as Agent and
Trustee for the Lenders, which Mortgage encumbers one hundred percent (100%) of
the Vessel "Delta Queen" (the "Vessel"); and

        C. In accordance with the provisions of Chapter 313 of Title 46 of the
United States Code, as amended (the "Act"), the Lenders and the Mortgagor have
requested that the Trustee serve as Trustee and Mortgagee for the benefit of the
Lenders under the Mortgage, and to hold the Mortgage to secure the Obligations
and such additional sums as the Mortgagor may be obligated to pay under and
pursuant to the Mortgage (collectively, the "Mortgage Obligations"). The Lenders
and the Mortgagor are sometimes referred to individually as a "Settlor" and
collectively as "Settlors"; and

        D. The Trustee has obtained the approval of the Maritime Administration,
United States Department of Transportation ("MARAD") to act as an "approved
trustee" pursuant to Public Law 89-346 and 46 U.S.C.A. Section 31328 to hold
security instruments and other items in connection with the financing of vessels
documented under the laws of the United States;

        NOW, THEREFORE, in consideration of the following declaration of trust
and of the mutual agreements herein set forth, the Settlors and the Trustee
hereby agree as follows:
<PAGE>   2
                                    ARTICLE I

        The Settlors, in furtherance of the aforesaid purposes and in order to
secure the payment and performance of the Mortgage Obligations, do hereby
constitute and appoint the Trustee to act as trustee under the Mortgage for the
benefit of the Lenders, and the Trustee does hereby declare that it does and
will hold as trustee all right, title and interest of the Lenders under the
Mortgage. The Mortgage Obligations are to be fully secured by the Mortgage and
the Mortgage is to be held by the Trustee in trust, for the benefit of the
Lenders upon the terms and conditions of this Indenture.

        Capitalized terms used herein without definition and otherwise defined
in the Credit Agreement shall have the same meanings used herein as therein.


                                   ARTICLE II

        This Indenture is irrevocable and may not be altered or amended in any
respect except as stated herein and may not be terminated except upon the
written agreement of the Settlors and the Trustee or upon the occurrence of
events stated herein.


                                   ARTICLE III

        To secure the Obligations owed by the Mortgagor to the Agent and the
Lenders, and the other Mortgage Obligations (including all obligations of
Borrower under the Credit Agreement) the Trustee shall be, or has been, granted
the Mortgage on the Vessel to be held in trust as provided herein.

                                   ARTICLE IV

        Under the terms of this Indenture, the Trustee shall have the following
rights and duties:

               (a) The Trustee shall hold the Mortgage for the benefit of the
        Agent and the Lenders as collateral security for the Mortgage
        Obligations owed to the Agent or the Lenders until such time as the
        Mortgage Obligations shall have been fully satisfied and all of the
        Mortgagor's obligations under and pursuant to the Mortgage Obligations
        and the Mortgage shall have extinguished.

               (b) The Trustee shall exercise all the rights and powers granted
        under the Mortgage except as limited herein or therein, and except as
        the Requisite Lenders (as defined in the Credit Agreement) may further
        request the Trustee to limit the exercise of its power and rights under
        the Mortgage, and the Trustee shall use its best efforts, at all times,
        to preserve its status as a "United States citizen" under 46 U.S.C.A.
        Section 802(c) and as otherwISE may be required by federal law, and to
        timely renew its status as an approved trustee under 46 CFR
        Section 221.35.


                                     Page 2
<PAGE>   3
               (c) Upon default by the Mortgagor under the Mortgage and notice
        thereof from the Requisite Lenders, the Trustee shall make demand upon
        the Mortgagor for payment of the Mortgage Obligations and full and
        punctual performance of its obligations under the Mortgage. If the
        Mortgagor should fail to make payment in full to the Trustee when due,
        the Trustee shall exercise its rights, as may be directed by the
        Requisite Lenders, to foreclose under the Mortgage and/or to exercise
        any other rights granted to the Trustee under the Mortgage or as be
        authorized under applicable law.

               (d) If the Mortgage Obligations shall be fully discharged,
        including, without limitation, all fees and expenses of the Trustee duly
        paid, and any obligations secured by the Mortgage fully discharged by
        the Mortgagor, and all of Lenders' obligations under the Credit
        Agreement or the Mortgage shall have terminated, the obligations and
        powers of Trustee hereunder shall terminate and the lien of the Mortgage
        shall be extinguished.

               (e) The Trustee, at the Requisite Lenders' election, upon default
        by Mortgagor under the Mortgage securing the Obligations, shall have the
        right to take and operate the Vessel and any other property, encumbered
        by the Mortgage as provided by the Mortgage, subject to prior written
        approval of the U.S. Secretary of Transportation to the extent required
        by 46 U.S.C.A. Sections 808 and 835, 46 U.S.C.A. 31328(e) and/or
        pursuant to 46 U.S.C.A. Section 31325(e) or to the extent authorized by
        the court pursuant to 46 U.S.C.A. Section 31325(e) provided, however,
        that this Indenture shall be subject to any statute of the United States
        and any regulations of MARAD, that may be in conflict herewith.

               (f) If the Trustee upon direction from the Requisite Lenders
        shall foreclose upon the Mortgage, the proceeds of the sale shall be
        applied as set forth in the Mortgage.

               (g) The Trustee shall be allowed to exercise such rights as
        provided under the Mortgage, including without limitation, the advance
        of funds or payment of expenses where such exercise will, in the
        reasonable determination of the Trustee, result in the preservation of
        the Vessel and be in the best interests of the Agent and the Lenders.

               (h) The Trustee is authorized to employ any custodian, receiver,
        attorney or other agent to assist the Trustee in the administration of
        this Indenture or the exercise of its rights under the Mortgage.

               (i) Upon the written direction of the Requisite Lenders, the
        Trustee is authorized to execute appropriate documentation releasing and
        discharging the Vessel from the lien of the Mortgage, and to execute,
        deliver and record any and all documents necessary in connection
        therewith.

               (j) The Mortgagor agrees to deliver to the Lenders copies of all
        notices, documents and other instruments required to be delivered to the
        Trustee under the Mortgage at the same time the same are delivered to
        Trustee.


                                     Page 3
<PAGE>   4
               (k) The Trustee shall fulfill all obligations imposed on it under
        46 CFR Part 221 and 46 U.S.C.A. Chapter 313, including the giving of any
        notices required under 46 CFR Section 221.37.


                                    ARTICLE V

        The Trustee may resign at any time by giving sixty (60) days' written
notice to the Settlors, provided, however, that such resignation shall only be
effective upon the appointment of a successor trustee, qualifying as an approved
trustee under the provisions of 46 U.S.C.A. Sections 808, 835 and/or 46
U.S.C.A. Section 31328(b) as listed by MARAD. In addition, the Requisite Lenders
may at any time remove the Trustee with or without cause by an instrument in
writing delivered to the Trustee, such removal to be effective upon the
acceptance of appointment of a successor trustee as hereinafter provided. In the
case of resignation or removal of the Trustee, the Requisite Lenders shall
appoint a successor trustee by an instrument signed by each such Lender, which
need not be executed by the Mortgagor. At such time as a successor trustee shall
be qualified, the Trustee shall assign all of its right, title and interest in
and to the Mortgage to said successor trustee, and thereafter each reference in
this Indenture to the Trustee shall be deemed to mean such successor trustee.
Any corporation into which the Trustee may be merged or converted with which it
may be consolidated or any corporation resulting from or surviving any merger,
conversion or consolidation to which the Trustee shall be a party, or any
corporation to which substantially all the corporate trust business of the
Trustee may be transferred, shall immediately become the successor trustee under
this Indenture, provided that such successor trustee qualifies as a "citizen of
the United States" within the meaning of 46 U.S.C.A. Section 802 and satisfies
the requirements of 46 U.S.C.A. 31328. Notwithstanding anything to the contrary
contained in this Indenture, in the event that the Trustee, or any successor
trustee shall at any time fail to be a citizen of the United States within the
meaning of 46 U.S.C.A. Section 802, such that the Vessel subjected to this
Indenture or the Mortgage should fail to qualify for coastwise trading, the
Trustee or successor trustee, whose United States citizenship status then
jeopardized the coastal trading license of the Vessel, shall be deemed to have
resigned immediately prior to such loss of United States citizenship, and shall
notify the Lenders thereof, and the Lenders shall thereafter designate a
successor trustee under the procedures set forth in this Indenture.


                                   ARTICLE VI

        No bond shall be required of the Trustee or of any Person appointed as
successor trustee for the faithful performance of its duties as trustee and
funds in the hands of the Trustee may be deposited with the Trustee without the
necessity of posting collateral.


                                     Page 4
<PAGE>   5
                                   ARTICLE VII

         The Trustee shall be reimbursed for all costs and expenses incurred in
the administration of this Indenture and in the exercise of its rights and
obligations under the Mortgage. Fees for usual or special services, including
services rendered hereunder as a result of a default by the Mortgagor under the
Mortgage or the obligation secured thereby will be reasonable. The Mortgagor
shall pay all of the Trustee's fees, costs, expenses, attorneys' and paralegals'
fees and charges. To the extent such fees and expenses are incurred during a
period of default under the Mortgage or Credit Agreement and are not paid timely
by the Mortgagor, the Lenders agree to pay or reimburse the Trustee for such
unpaid amounts.


                                  ARTICLE VIII

        The validity, construction and interpretation of this Indenture, and the
administration of the trust created hereunder, shall be governed by the laws of
the State of Louisiana (without regard to the laws applicable to conflicts or
choice of law) except to the extent preempted by federal or maritime law of the
United States. This Indenture and any amendments, waivers, consents or
supplements may be executed in counterparts, each of which when so executed and
delivered shall be deemed an original, but all such counterparts together shall
constitute but one and the same instrument.


                                   ARTICLE IX

        If any provision of this Indenture is contrary to, prohibited by or
deemed invalid under any applicable law or regulation, such provision shall be
inapplicable and deemed omitted to the extent so contrary, prohibited or
invalid, but the remainder of this Indenture shall not be invalidated thereby
and shall be given full force and effect so far as possible.


                                    ARTICLE X

        The Mortgagor hereby agrees to defend, indemnify and hold the Trustee
and its successors, assigns, legal representatives and agents, harmless from and
against any and all liabilities, obligations, losses, damages, fines, penalties,
taxes, claims, actions, suits, costs or disbursements (including without
limitation, reasonable attorneys' fees and expenses) of any kind or nature
whatsoever (except such arising from the wilful misconduct or gross negligence
on the part of the Trustee) incurred by the Trustee which may be imposed on,
incurred or assessed against the Trustee arising out of or in connection with
the acceptance or administration of the Indenture created hereby.


                                     Page 5
<PAGE>   6
                                   ARTICLE XI

        The Lenders shall have the right to sell or assign the Obligations, and
any part thereof, with or without recourse, in accordance with the provisions of
the Credit Agreement and upon presentation to the Trustee of such instrument(s)
and/or other documents required pursuant to the Credit Agreement evidencing such
sale or assignment, in form reasonably satisfactory to the Trustee, such
purchaser or assignee of the Obligations shall succeed to all of the rights and
obligations of the Lenders hereunder.


                                   ARTICLE XII

        All notices, consents, approvals, requests, demands and other
communications hereunder shall be in writing and shall be sent by mail (by
registered or certified mail, return receipt requested), Federal Express or
similar overnight delivery service, telecopy or hand delivery, as follows:

               (a)     To the Owner:

                       c/o The Delta Queen Steamboat Co.
                       Two North Riverside Plaza, 2nd Floor
                       Chicago, IL  60606
                       Attention: Jordan Allen
                       Telephone:     (312) 466-6202
                       Telecopy:      (312) 466-6151

               with a copy to:

                       Rosenberg & Liebentritt, P.C.
                       Two North Riverside Plaza, Suite 1600
                       Chicago, IL  60606
                       Attention: Jim Phipps
                       Telephone:     (312) 466-3623
                       Telecopy:      (312) 575-7000

                       and

                       Adams and Reese, L.L.P.
                       4500 One Shell Square
                       New Orleans, Louisiana 70139
                       Attention: Louis A. Wilson, Jr.
                       Telephone:     (504) 581-3234
                       Telecopy:      (504) 566-0210


                                     Page 6
<PAGE>   7
               (b)     To the Mortgagee:

                       The Chase Manhattan Bank
                       c/o Chase Securities Inc.
                       10 South LaSalle Street
                       Chicago, Illinois  60603
                       Attention: Jon Hinard
                       Telephone:     (312) 807-4550
                       Telecopy:      (312) 807-4046

        with a copy to:

                       Sidley & Austin
                       One First National Plaza,
                       Chicago, Illinois 60603
                       Attention: Douglas H. Williams
                       Telephone:     (312) 853-7667
                       Telecopy:      (312) 853-7036


with notice, request or communication hereunder deemed to have been given when
delivered in person or by courier service, upon receipt of a telecopy or telex
or upon delivery or refusal to accept delivery if deposited in the United States
mail (registered or certified, with postage prepaid and properly addressed). Any
party may change the Person or address to whom or which the notices are to be
given hereunder, by notice duly given hereunder.

                                  [END OF PAGE]


                                     Page 7
<PAGE>   8
                            SIGNATURE PAGE - TRUSTEE


         IN WITNESS WHEREOF, the parties have caused this Indenture to be
executed by their duly authorized officers as of the date first above written.


WITNESSES:                                 THE CHASE MANHATTAN BANK, NOT IN ITS
                                           INDIVIDUAL CAPACITY, BUT AS TRUSTEE

                                            /s/ STEVEN J. FALISKI
------------------------------------       ------------------------------------
               
                                           Name: STEVEN J. FALISKI
------------------------------------            -------------------------------
                                           Title: Vice President
                                                -------------------------------


                                     Page 8
<PAGE>   9
                            SIGNATURE PAGE - SETTLORS

         IN WITNESS WHEREOF, the parties have caused this Indenture to be
executed by their duly authorized officers as of the date first above written.


WITNESSES:                                 THE CHASE MANHATTAN BANK, AS
                                           LENDER


                                            /s/ STEVEN J. FALISKI
------------------------------------       ------------------------------------
               
                                           Name: Steven J. Faliski
------------------------------------            -------------------------------
                                           Title: Vice President 
                                                -------------------------------



                                           HIBERNIA NATIONAL BANK, AS LENDER

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



                                           BANK ONE, LOUISIANA, NATIONAL
                                           ASSOCIATION, AS LENDER

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


                                     Page 9
<PAGE>   10
WITNESSES:                                  CREDIT AGRICOLE INDOSUEZ, AS LENDER

                                            /s/ KATHERINE L. ABBOTT
------------------------------------       ------------------------------------
               
                                           Name: Katherine L. Abbott
------------------------------------            -------------------------------
                                           Title: First Vice President
                                                -------------------------------


                                           THE BANK OF NEW YORK, AS LENDER
                                            /s/ RICHARD RAFFETTO 
------------------------------------       ------------------------------------
               
                                           Name: Richard Raffetto
------------------------------------            -------------------------------
                                           Title: Vice President 
                                                -------------------------------


                                           GREAT RIVER CRUISE LINE, L.L.C.

                                           BY: THE DELTA QUEEN STEAMBOAT CO.,
                                               A MANAGING MEMBER

                                            /s/ JORDAN B. ALLEN         
------------------------------------       ------------------------------------
               
                                           Name:  Jordan B. Allen         
------------------------------------       Title: Executive Vice President


                                           BY: DQSB II, INC., A MANAGING MEMBER

                                            /s/ JORDAN B. ALLEN         
------------------------------------       ------------------------------------
               
                                           Name:  Jordan B. Allen         
------------------------------------       Title: Executive Vice President



                                    Page 10
<PAGE>   11
                            ACKNOWLEDGMENT OF TRUSTEE


STATE OF ILLINOIS

COUNTY OF COOK


         On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                             /s/ STEVEN J. FALISKI
                  ---------------------------------------------
                        

appearing herein in his capacity as Vice President of The Chase Manhattan Bank,
a New York banking corporation, as Trustee under the aforesaid Trust Indenture
(the "Indenture"), to me personally known to be the identical person whose name
is subscribed to the Indenture, who declared and acknowledged, that he executed
the same on behalf of such with full authority, and that the instrument is the
free act and deed of such Bank, executed for the uses, purposes and benefits
therein expressed.




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


                      ------------------------------------
                                  NOTARY PUBLIC



                                    Page 11
<PAGE>   12
                           ACKNOWLEDGMENT OF SETTLOR


STATE OF ILLINOIS

COUNTY OF COOK


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                             /s/ STEVEN J. FALISKI
                  ---------------------------------------------


appearing herein in his capacity as Vice President of The Chase Manhattan Bank,
a New York banking corporation, as Lender under the aforesaid Trust Indenture
(the "Indenture"), to me personally known to be the identical person whose name
is subscribed to the Indenture, who declared and acknowledged, that he executed
the same on behalf of such with full authority, and that the instrument is the
free act and deed of such Bank, executed for the uses, purposes and benefits
therein expressed.



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


                      ------------------------------------
                                  NOTARY PUBLIC



                                    Page 12
<PAGE>   13
                            ACKNOWLEDGMENT OF SETTLOR


STATE OF LOUISIANA

PARISH OF ORLEANS


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                           /s/ WILLIAM P. HERRINGTON
                  ---------------------------------------------


appearing herein in his capacity as Sr. Vice President of Hibernia National
Bank, as Lender under the aforesaid Trust Indenture (the "Indenture"), to me
personally known to be the identical person whose name is subscribed to the
Indenture, who declared and acknowledged, that he executed the same on behalf of
such with full authority, and that the instrument is the free act and deed of
such Bank, executed for the uses, purposes and benefits therein expressed.


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


                      ------------------------------------
                                  NOTARY PUBLIC



                                    Page 13
<PAGE>   14
                            ACKNOWLEDGMENT OF SETTLOR


STATE OF LOUISIANA

PARISH OF ORLEANS


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                               /s/ LIZETTE TERRAL
                  ---------------------------------------------


appearing herein in his capacity as Sr. Vice President of Bank One, Louisiana,
N.A., as Lender under the aforesaid Trust Indenture (the "Indenture"), to me
personally known to be the identical person whose name is subscribed to the
Indenture, who declared and acknowledged, that he executed the same on behalf of
such with full authority, and that the instrument is the free act and deed of
such Bank, executed for the uses, purposes and benefits therein expressed.

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


                     -------------------------------------
                                 NOTARY PUBLIC




                                    Page 14
<PAGE>   15
                            ACKNOWLEDGMENT OF SETTLOR


STATE OF ILLINOIS

COUNTY OF COOK


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                                /s/ DAVID BOUHL
                  ---------------------------------------------
                                 

appearing herein in his capacity as First VP of Credit Agricole Indosuez, as
Lender under the aforesaid Trust Indenture (the "Indenture"), to me personally
known to be the identical person whose name is subscribed to the Indenture, who
declared and acknowledged, that he executed the same on behalf of such with full
authority, and that the instrument is the free act and deed of such Bank,
executed for the uses, purposes and benefits therein expressed.


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


                      ------------------------------------
                                  NOTARY PUBLIC



                                    Page 15
<PAGE>   16
                            ACKNOWLEDGMENT OF SETTLOR


STATE OF NEW YORK

COUNTY OF NEW YORK


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                              /s/ RICHARD RAFFETTO
                  ---------------------------------------------
                       

appearing herein in his capacity as Vice President of The Bank of New York, as
Lender under the aforesaid Trust Indenture (the "Indenture"), to me personally
known to be the identical person whose name is subscribed to the Indenture, who
declared and acknowledged, that he executed the same on behalf of such with full
authority, and that the instrument is the free act and deed of such Bank,
executed for the uses, purposes and benefits therein expressed.



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


                      ------------------------------------
                                  NOTARY PUBLIC



                                    Page 16
<PAGE>   17
                            ACKNOWLEDGMENT OF SETTLOR


STATE OF ILLINOIS

COUNTY OF COOK


        On this 25th day of February, 1999, before me, the undersigned
authority, duly commissioned and qualified in and for the aforesaid
jurisdiction, personally came and appeared:

                                 JORDAN B. ALLEN

the duly authorized Executive Vice President and representative of THE DELTA
QUEEN STEAMBOAT CO. and DQSB II, INC., which said corporations are the sole
managing members of GREAT RIVER CRUISE LINE, L.L.C., a Delaware limited
liability company, as Settlor under the aforesaid Trust Indenture (the
"Indenture"), to me personally known to be the identical person whose name is
subscribed to the Indenture, who declared and acknowledged, that he executed the
same on behalf of such with full authority, and that the instrument is the free
act and deed of such Bank, executed for the uses, purposes and benefits therein
expressed.


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


                      ------------------------------------
                                  NOTARY PUBLIC





                                    Page 17