<PAGE>

                                                                     EXHIBIT 4.4
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                          TRICO MARINE SERVICES, INC.
                         TRICO MARINE OPERATORS, INC.
                           TRICO MARINE ASSETS, INC.

                                      and

                          the Guarantors named herein


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


                             SERIES A AND SERIES B

                         8-1/2% SENIOR NOTES DUE 2005


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



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


                         FIRST SUPPLEMENTAL INDENTURE
                     AND AMENDMENT - SUBSIDIARY GUARANTEE


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



                   CHASE BANK OF TEXAS NATIONAL ASSOCIATION

                                    Trustee



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


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<PAGE>
 
                         FIRST SUPPLEMENTAL INDENTURE


     This FIRST SUPPLEMENTAL INDENTURE, dated as of March 19, 1998 (this
"Supplemental Indenture"), is among Trico Marine Services, Inc., a Delaware
corporation (the "Company"), each of the parties identified under the caption
"Guarantors" on the signature page hereto (the "Guarantors") and Chase Bank of
Texas National Association, as successor to Texas Commerce Bank National
Association, as Trustee.

                                   RECITALS

     WHEREAS, the Company, Trico Marine Operators, Inc., Trico Marine Assets,
Inc. and the Trustee entered into an Indenture, dated as of July 21, 1997 (the
"Indenture"), pursuant to which the Company issued $110,000,000 in principal
amount of 8-1/2% Senior Notes due 2005 (the "Notes"); and

     WHEREAS, Section 9.01(f) of the Indenture provides that the Company and the
Trustee may amend or supplement the Indenture in order to execute a guarantee (a
"Subsidiary Guarantee") to comply with Section 10.02 thereof without the consent
of the Holders of the Notes; and

     WHEREAS, all acts and things prescribed by the Indenture, by law and by the
Certificate of Incorporation, bylaws or other similar organizational documents
of the Company, of the Guarantors and of the Trustee necessary to make this
Supplemental Indenture a valid instrument legally binding on the Company, the
Guarantors and the Trustee, in accordance with its terms, have been duly done
and performed;

     NOW, THEREFORE, to comply with the provisions of the Indenture and in
consideration of the above premises, the Company, the Guarantors and the Trustee
covenant and agree for the equal and proportionate benefit of the respective
Holders of the Notes as follows:

                                   ARTICLE 1

     Section 1.1 This Supplemental Indenture is supplemental to the Indenture
and does and shall be deemed to form a part of, and shall be construed in
connection with and as part of, the Indenture for any and all purposes.

     Section 1.2 This Supplemental Indenture shall be deemed to have become
effective as of December 2, 1997 (the "Effective Date").

                                   ARTICLE 2

     From the Effective Date, in accordance with Section 10.02 and by executing
this Supplemental Indenture and the accompanying Subsidiary Guarantee (a copy of
which is attached

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<PAGE>
 
hereto), the Guarantors whose signatures appear below shall be subject to the
provisions of the Indenture to the extent provided for in Article 10 thereunder.

                                   ARTICLE 3

     Section 3.01 Except as specifically modified herein, the Indenture and the
Notes are in all respects ratified and confirmed (mutatis mutandis) and shall
remain in full force and effect in accordance with their terms with all
capitalized terms used herein without definition having the same respective
meanings ascribed to them as in the Indenture.

     Section 3.02 Except as otherwise expressly provided herein, no duties,
responsibilities or liabilities are assumed, or shall be construed to be
assumed, by the Trustee by reason of this Supplemental Indenture. This
Supplemental Indenture is executed and accepted by the Trustee subject to all
the terms and conditions set forth in the Indenture with the same force and
effect as if those terms and conditions were repeated at length herein and made
applicable to the Trustee with respect hereto.

     Section 3.03 THE INTERNAL LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE
USED TO CONSTRUE THIS SUPPLEMENTAL INDENTURE, THE NOTES AND THE SUBSIDIARY
GUARANTEES.

     Section 3.04 The parties may sign any number of copies of this Supplemental
Indenture. Each signed copy shall be an original, but all of such executed
copies together shall represent the same agreement.

     IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed, all as of the date first written above.

                              TRICO MARINE SERVICES, INC.



                              By:     /s/ VICTOR M. PEREZ
                                  -------------------------------------
                                          Victor M. Perez
                                     Vice President and Chief
                                         Financial Officer

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                              GUARANTORS:

                              TRICO MARINE INTERNATIONAL
                                   HOLDINGS, B.V.



                              By:       /s/ RONALD O. PALMER
                                   -----------------------------------
                                   Name:  Ronald O. Palmer
                                   Title: Managing Director

                              SAEVIK SUPPLY ASA



                              By:       /s/ KIM DOBROWEN
                                   -----------------------------------
                                   Name:  Kim Dobrowen
                                   Title: Director

                              SAEVIK SHIPPING AS



                              By:       /s/ KIM DOBROWEN
                                   -----------------------------------
                                   Name:  Kim Dobrowen
                                   Title: Director

                              TRUSTEE:

                                   CHASE BANK OF TEXAS NATIONAL
                                    ASSOCIATION, as Trustee



                              By:      /s/ REBECCA A. NEWMAN
                                   -----------------------------------
                                   Name:  Rebecca A. Newman
                                   Title: Vice President and Trust Officer

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                             SUBSIDIARY GUARANTEE

     Subject to Section 10.06 of the Indenture, dated July 21, 1997 (the
"Indenture") by and among Trico Marine Services, Inc., a Delaware corporation
(the "Company"), Trico Marine Operators, Inc., a Louisiana corporation, Trico
Marine Assets, Inc., a Delaware corporation and Texas Commerce Bank National
Association, as trustee, each of the undersigned (collectively, the "New
Guarantors" and each a "New Guarantor") hereby, jointly and severally,
unconditionally guarantees to each Holder of a Note authenticated and delivered
by the Trustee and to the Trustee and its successors and assigns, irrespective
of the validity and enforceability of the Indenture, the Notes and the
Obligations of the Company under the Notes or under the Indenture, that: (a) the
principal of, premium, if any, interest and Liquidated Damages, if any, on the
Notes will be promptly paid in full when due, subject to any applicable grace
period, whether at maturity, by acceleration, redemption or otherwise, and
interest on overdue principal, premium, if any, (to the extent permitted by law)
interest on any interest, if any, and Liquidated Damages, if any, on the Notes
and all other payment Obligations of the Company to the Holders or the Trustee
under the Indenture or under the Notes will be promptly paid in full and
performed, all in accordance with the terms hereof; and (b) in case of any
extension of time of payment or renewal of any Notes or any of such other
payment Obligations, the same will be promptly paid in full when due or
performed in accordance with the terms of the extension or renewal, subject to
any applicable grace period, whether at stated maturity, by acceleration,
redemption or otherwise. Failing payment when so due of any amount so guaranteed
or any performance so guaranteed for whatever reason, the New Guarantors will be
jointly and severally obligated to pay the same immediately. An Event of Default
under the Indenture or the Notes shall constitute an event of default under this
Subsidiary Guarantee, and shall entitle the Holders to accelerate the
Obligations of the New Guarantors hereunder in the same manner and to the same
extent as the Obligations of the Company. The New Guarantors hereby agree that
their Obligations hereunder shall be unconditional, irrespective of the
validity, regularity or enforceability of the Notes or the Indenture, the
absence of any action to enforce the same, any waiver or consent by any Holder
with respect to any provisions hereof or thereof, the recovery of any judgment
against the Company, any action to enforce the same or any other circumstance
which might otherwise constitute a legal or equitable discharge or defense of a
New Guarantor. Each New Guarantor hereby waives diligence, presentment, demand
of payment, filing of claims with a court in the event of insolvency or
bankruptcy of the Company, any right to require a proceeding first against the
Company, protest, notice and all demands whatsoever and covenants that this
Subsidiary Guarantee will not be discharged except by complete performance of
the Obligations contained in the Notes and the Indenture. If any Holder or the
Trustee is required by any court or otherwise to return to the Company, the
Guarantors, the New Guarantors or any Note Custodian, Trustee, liquidator or
other similar official acting in relation to either the Company, the Guarantors
or the New Guarantors, any amount paid by the Company, the Guarantors or any New
Guarantor to the Trustee or such Holder, this Subsidiary Guarantee, to the
extent theretofore discharged, shall be reinstated in full force and effect.
Each New Guarantor agrees that it shall not be entitled to, and hereby waives,
any right of subrogation in relation to the Holders in respect of any
Obligations guaranteed hereby. Each New Guarantor further agrees that, as
between the New Guarantors, on the one hand, and the Holders and the Trustee, on
the other hand, (a) the maturity of the Obligations

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<PAGE>
 
guaranteed hereby may be accelerated as provided in Article 6 of the Indenture
for the purposes of this Subsidiary Guarantee, notwithstanding any stay,
injunction or other prohibition preventing such acceleration in respect of the
Obligations guaranteed thereby, and (b) in the event of any declaration of
acceleration of such Obligations as provided in Article 6 of the Indenture, such
Obligations (whether or not due and payable) shall forthwith become due and
payable by the New Guarantor for the purpose of this Subsidiary Guarantee. The
New Guarantors shall have the right to seek contribution from any non-paying
Guarantor or New Guarantor as long as the exercise of such right does not impair
the rights of the Holders under this or any other Subsidiary Guarantee.

     The obligations of the New Guarantor to the Holders and to the Trustee
pursuant to this Subsidiary Guarantee and the Indenture are expressly set forth
in Article 10 of the Indenture, and reference is hereby made to such Indenture
for the precise terms of this Subsidiary Guarantee. The terms of Article 10 of
the Indenture are incorporated herein by reference. This Subsidiary Guarantee is
subject to release as and to the extent provided in Sections 10.4 and 10.5 of
the Indenture.

     This is a continuing Guarantee and shall remain in full force and effect
and shall be binding upon each New Guarantor and its respective successors and
assigns to the extent set forth in the Indenture until full and final payment of
all of the Company's Obligations under the Notes and the Indenture and shall
inure to the benefit of the successors and assigns of the Trustee and the
Holders and, in the event of any transfer or assignment of rights by any Holder
or the Trustee, the rights and privileges herein conferred upon that party shall
automatically extend to and be vested in such transferee or assignee, all
subject to the terms and conditions hereof. This is a Subsidiary Guarantee of
payment and not a guarantee of collection.

     This Subsidiary Guarantee shall not be valid or obligatory for any purpose
until the certificate of authentication on the Note upon which this Subsidiary
Guarantee is noted shall have been executed by the Trustee or an authenticating
agent under the Indenture by the manual signature of one of its authorized
officers.

     For purposes hereof, each New Guarantor's liability shall be limited to the
lesser of (i) the aggregate amount of the Obligations of the Company under the
Notes and the Indenture, (ii) the amount, if any, which would not have (A)
rendered such New Guarantor "insolvent" (as such term is defined in the
Bankruptcy Law and in the Debtor and Creditor Law of the State of New York) or
(B) left such New Guarantor with unreasonably small capital at the time its
Subsidiary Guarantee of the Notes was entered into and (iii) in the case of
Saevik Supply ASA and Saevik Shipping AS, the maximum amount permitted under
applicable Norwegian law; provided that, it will be a presumption in any lawsuit
or other proceeding in which a New Guarantor is a party that the amount
guaranteed pursuant to the Subsidiary Guarantee is the amount set forth in
clause (i) above unless any creditor, or representative of creditors of such New
Guarantor, or debtor in possession or trustee in bankruptcy of such New
Guarantor, otherwise proves in such a lawsuit that the aggregate liability of
the New Guarantor is limited to the amount set forth in clauses (ii) or (iii)
above. The Indenture provides that, in making any determination as to the
solvency or sufficiency of capital of a New Guarantor in accordance with the
previous sentence, the right of the New Guarantors to contribution

                                      -5-
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from the Guarantors and other New Guarantors and any other rights such New
Guarantors may have, contractual or otherwise, shall be taken into account.

     Capitalized terms used and not defined herein have the same meanings given
in the Indenture unless otherwise indicated.

                              TRICO MARINE INTERNATIONAL
                                   HOLDINGS, B.V.



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

                              SAEVIK SUPPLY ASA



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

                              SAEVIK SHIPPING AS



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

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