<PAGE>   1
                                                                     Exhibit 4.4

                                 PROMISSORY NOTE
$373,845.00                                                   New York, New York
                                                                   June 16, 1998

      FOR VALUE RECEIVED, the undersigned, OMI Corp., a Delaware Corporation
("Marine"), hereby promises to pay to the order of OMI Corporation ("OMI"), at
its office at One Station Place, Stamford, CT 06902 (or such other place as OMI
may direct from time to time), in lawful money of the United States and in
immediately available funds, the principal amount of three hundred seventy three
thousand eight hundred forty five Dollars ($373,845.00) plus, interest on said
principal amount, from the date hereof. Payments of principal and interest shall
be made in the amounts and on the dates set forth on the attached Annex A.

      Marine may prepay the outstanding principal of this Note, in whole, but
not in part, upon 10 days' prior written notice to the holder of this Note.
Prepayment hereunder shall be accompanied by payment of accrued interest
calculated from the date of the immediately prior installment payment to the
date of the next scheduled payment adjusted, pro rata, to the date of
prepayment.

      Marine shall pay on demand interest on the outstanding unpaid principal
amount of this Note that is not paid within 5 business days of when due and on
the unpaid amount of all interest fees and other amounts then due and payable
hereunder that is not paid within 5 business days of when due from the due date
thereof to the date paid, at a rate per annum equal to 3% per annum above the
rate of interest per annum borne by this Note.

      Marine is a duly organized and validly existing corporation, and is in
good standing under the laws of Delaware and has the corporate power and
authority to execute, deliver and carry out the terms and provisions of this
Note and has taken all necessary corporate action to authorize the execution,
delivery and performance of this Note. This Note constitutes the legal, valid
and binding obligation of Marine enforceable in accordance with its terms,
except to the extent that the enforceability thereof may be limited by
applicable bankruptcy, insolvency, reorganization, moratorium or similar laws
generally affecting creditors' rights and by equitable principles (regardless of
whether enforcement is sought in equity or at law).

      Neither the execution, delivery or performance by Marine of this Note, nor
compliance by it with the terms and provisions hereof, (i) will contravene any
applicable provision of any law, statute, rule or regulation, or any order,
writ, injunction or decree of any court or governmental instrumentality, (ii)
will conflict or be inconsistent with or result in any breach of, any of the
terms, covenants, conditions or provisions of, or constitute a default under, or
result in the creation or imposition of (or the obligation to create or impose)
any Lien upon any of the property or assets of Marine pursuant to the terms of
any indenture, mortgage, deed of trust, credit agreement or loan agreement, or
any other material agreement, contact or instrument to which Marine is a party
or by which it or any of its property or assets are bound or to which it may be
subject or
<PAGE>   2

(iii) will violate any provision of the certificate or articles of incorporation
or by-laws (or equivalent organizational documents), as the case may be, of
Marine.

      Upon the occurrence of any of the following specified events (each an
"Event of Default"):

      1.    Marine shall fail to pay any of the principal of this Note on the
            date when due or fail to pay any of the interest on this Note within
            5 business days of the date when due; or

      2.    Marine shall (i) default in any payment of principal of or interest
            on any indebtedness or contingent obligation (other than its
            obligation under this Note) or (ii) default in the observance or
            performance of any agreement or condition relating to any
            indebtedness or contingent obligation (other than this Note) or
            contained in any instrument or agreement evidencing, securing or
            relating thereto, or any other event shall occur, the effect of
            which is to permit such indebtedness or contingent obligation to be
            declared due and payable or such indebtedness or contingent
            obligation shall otherwise become due or required to be prepaid
            prior to its stated maturity (determined without regard to whether
            any notice is required); provided, that is shall not constitute an
            Event of Default pursuant to clause (i) or (ii) above unless the
            aggregate principal amount of all such indebtedness or contingent
            obligations as described in clauses (i) and (ii), inclusive, exceeds
            $100,000 at any one time; or

      3.    (a) Marine shall (i) commence any case, proceeding or other action
            under any existing or future law of any jurisdiction, domestic or
            foreign, relating to bankruptcy, insolvency, reorganization, or
            relief of debtors, seeking to have an order for relief entered with
            respect to it, or seeking to adjudicate it a bankrupt or insolvent,
            or seeking reorganization, arrangement, adjustment, winding-up,
            liquidation, dissolution, composition, or other relief with respect
            to it or its debts, or (ii) commence any case, proceeding, or other
            action seeking appointment of a receiver, trustee, custodian, or
            other similar official for it or for all or any substantial part of
            its assets, or (iii) make a general assignment for the benefit of
            its creditors; (b) there shall be commenced against Marine any case,
            proceeding or other action of a nature referred to in clause (a)
            above that (i) results in the entry of an order for relief or any
            such adjudication or appointment, or (ii) remains undismissed,
            undischarged, or unbonded for a period of sixty (60) days; (c) there
            shall be commenced against Marine any case, proceeding or other
            action seeking issuance of a warrant of attachment, execution,
            distraint, or similar process against all or any substantial part of
            its assets that results in the entry of an order for any such relief
            that shall not have been vacated, discharged, or stayed or bonded
            pending appeal within sixty (60) days from the entry thereof; (d)
            Marine shall take any action in furtherance of, or indicating its
            consent to, approval of, or acquiescence in, any of the acts set
            forth in clause (a), (b), or (c) previously; or (e) Marine shall
            generally not, or shall be unable to, or shall admit in writing its
            inability to, pay its debts as they become due; or


                                      -2-
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      4.    One or more final judgments or decrees shall be entered against
            Marine involving a liability not paid or fully covered by insurance
            in excess of $100,000 for all such judgments and decrees and all
            such judgments or decrees shall not have been vacated, discharged,
            or stayed or bonded pending appeal within sixty (60) days from the
            entry thereof.

THEN, the holder hereof may declare the outstanding principal balance hereof
immediately due and payable and Marine shall immediately pay to the holder all
such amounts, with interest accrued but unpaid thereon to the date of payment in
full at the applicable rate provided herein.

      Marine, for itself, its successors and assigns, hereby waives diligence,
presentment, protest, and demand and notice of protest, demand, dishonor, and
nonpayment of this Note.

      Neither acceptance by the holder hereof of partial or delinquent payment
nor any failure on the part of the holder to exercise, or any delay in
exercising, any right under this Note shall operate as a waiver of any
obligation of Marine or any right of the holder, and no single or partial
exercise of any right under this Note shall preclude any other or further
exercise thereof or the exercise of any other right. No waiver, amendment,
alteration or other modification of any provision of this Note shall in any
event be effective unless the same shall be in writing and signed by the holder.
The remedies provided in this Note are cumulative and not exclusive of any
remedies provided by law. All of the covenants, provisions, and conditions
herein contained are made on behalf of, and shall apply to and bind the
respective distributees, personal representatives, successors, and assigns of
Marine, jointly and severally. Marine agrees to pay all collection expenses,
court costs, and reasonable attorney fees and disbursements (whether or not
litigation is commenced) that may be incurred in connection with the collection
or enforcement of this Note.

      This Note shall be governed by and construed in accordance with the laws
of the State of New York, without giving effect to conflicts of laws or
principles thereof.

                                        OMI CORP.
                                        a Delaware Corporation


                                        By: /s/ V. de Sostca
                                           -------------------------------------
                                           Name:  Vincent de Sostca
                                           Title: S.V.P.


                                      -3-
<PAGE>   4

                                                                         ANNEX A

<TABLE>
<CAPTION>
                                                                   Total Payment
                     Outstanding    Principal                      Due (Interest
Payment Date           Principal     Payment   Interest Payment  Plus Principal)
------------           ---------     -------   ----------------  ---------------
<C>                  <C>            <C>        <C>               <C>    
l6 June 1998         373,845.00                                             0
01 November 1998     373,845.00     37,384.50     14,954.00         52,338.50
01 May 1999          336,460.50     37,384.50     13,458.00         50,842.50
01 November 1999     299,076.00     37,384.50     11,963.00         49,347.50
01 May 2000          261,691.50     37,384.50     10,468.00         47,852.50
01 November 2000     224,307.00     37,384.50      8,972.00         46,356.50
01 May 2001          186,922.50     37,384.50      7,477.00         44,861.50
01 November 2001     149,538.00     37,384.50      5,982.00         43,366.50
01 May 2002          112,153.50     37,384.50      4,486.00         41,870.50
01 November 2002      74,769.00     37,384.50      2,991.00         40,375.50
01 May 2003           37,384.50     37,384.50      1,495.00         38,879.50
                    -----------   -----------      --------       -----------
Total:                            $373,845.00    $82,246.00       $456,091.00
</TABLE>