SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20552

                                   ----------
                                   FORM 10-Q
                                   ----------

(MARK ONE)

|X|  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
     ACT OF 1934 For the quarterly period ended December 31, 1998

|_|  TRANSITION REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
     EXCHANGE ACT OF 1934

  For the transition period from _____________________ to ____________________


                           COMMISSION FILE NO. 0-22499

                            BAYONNE BANCSHARES, INC.
             (Exact name of registrant as specified in its charter)

           Delaware                                          22-3511899
(State or other jurisdiction of                            (I.R.S. Employer
 incorporation or organization)                          Identification Number)

                     568 Broadway, Bayonne, New Jersey 07002
                    (Address of principal executive offices)

Registrant's telephone number, including area code: (201) 437-1000


--------------------------------------------------------------------------------
Former name, former address and former fiscal year, if changed since last report

     Indicate  by check |X|  whether  the  Registrant  (1) has filed all reports
required to be filed by Section 13 or 15 (d) of the  Securities  Exchange Act of
1934  during  the  preceding  12 months  (or for such  shorter  period  that the
Registrant was required to file such reports),  and (2) has been subject to such
filing requirements for the past 90 days. Yes |X| No | |

           AS OF FEBRUARY 12, 1999, THERE WERE 8,255,824 SHARES OF THE
                      REGISTRANT'S COMMON STOCK OUTSTANDING



<PAGE>

                            BAYONNE BANCSHARES, INC.

                                      INDEX

PART I.    FINANCIAL INFORMATION                                            Page
                                                                            ----
Item 1.    Consolidated Financial Statements

           Consolidated Statements of Financial Condition as of                1
           December 31, 1998 and March 31, 1998

           Consolidated Statements of Income for the three and nine
           months ended December 31, 1998 and 1997                             2

           Consolidated Statements of Stockholders' Equity for the nine        3
           months ended December 31, 1998 and 1997

           Consolidated Statements of Cash Flows for the nine months         4-5
           ended December 31, 1998 and 1997

           Notes to Consolidated Financial Statements                        6-9

Item 2.    Management's Discussion and Analysis of Financial                9-15
           Condition and Results of Operations

Item 3.    Quantitative and Qualitative Disclosures About Market Risk         15

PART II.   OTHER INFORMATION                                               15-16



<PAGE>

PART I    FINANCIAL INFORMATION

Item 1

                       Consolidated Financial Statements

                            BAYONNE BANCSHARES, INC.
                 CONSOLIDATED STATEMENTS OF FINANCIAL CONDITION
                                 (in thousands)

                                                        December 31,   March 31,
                                                            1998         1998
                                                        -----------   ---------
ASSETS

Cash and cash equivalents:
  Cash on hand and in banks                              $   7,796    $   4,712
  Deposits with financial institutions                          --       11,900
  AMF short-term fund                                            5            5
                                                         ---------    ---------
    Total cash and cash equivalents                          7,801       16,617


Securities available for sale, at market value             314,096      362,778
Securities held to maturity                                 11,392       10,274
Loans receivable, net                                      295,838      235,465
Accrued interest receivable, net                             3,888        4,089
Federal Home Loan Bank stock, at cost                       10,511        7,460
Real estate acquired in settlement of loans                    651          330
Office properties and equipment, net                         5,435        5,351
Prepaid expenses                                             1,014          672
Other assets                                                 3,899        3,022
                                                         ---------    ---------
 Total Assets                                            $ 654,525    $ 646,058
                                                         =========    =========

LIABILITIES AND STOCKHOLDERS' EQUITY

Liabilities:
 Deposits                                                $ 419,609    $ 423,545
 Borrowings                                                144,825      115,000
 ESOP loan                                                     217          380
 Advance payment by borrowers for taxes and insurance        2,532        3,754
 Accrued expenses and other liabilities                      5,358        4,730
                                                         ---------    ---------
  Total Liabilities                                      $ 572,541    $ 547,409
                                                         =========    =========

Stockholders' equity:
 Common stock                                                   92           91
 Additional paid in capital                                 61,352       60,246
 Common stock acquired by ESOP and MRP                      (6,827)      (4,301)
 Retained earnings-substantially restricted                 45,664       43,702
 Treasury stock-888,683 shares                             (14,764)          --
 Accumulated other comprehensive loss                       (3,533)      (1,089)
                                                         ---------    ---------
  Total stockholders' equity                                81,984       98,649
                                                         ---------    ---------
   Total liabilities and stockholders' equity            $ 654,525    $ 646,058
                                                         =========    =========

        See accompanying notes to the consolidated financial statements.

                                       1

<PAGE>

                            Bayonne Bancshare, Inc.
                                and Subsidiaries
                       Consolidated Statements of Income
                                 (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                                                             Three Months                       Nine Months
                                                                          Ended December 31,                 Ended December 31,
                                                                     --------------------------          --------------------------
                                                                       1998              1997              1998              1997
                                                                     --------          --------          --------          --------
<S>                                                                  <C>               <C>               <C>               <C>     
Interest and dividend income:
  Loans                                                              $  5,849          $  4,904          $ 16,855          $ 14,705
  Securities available for sale                                         4,548             4,759            14,486            14,330
  Securities held to maturity                                             367               302             1,071               904
  Overnight deposits with financial institutions                           77               171               213               383
                                                                     --------          --------          --------          --------
Total interest and dividend income                                     10,841            10,136            32,625            30,322
                                                                     --------          --------          --------          --------

Interest expense:
  Interest on deposits                                                  4,485             5,011            13,638            15,388
  Interest on other borrowings                                          1,997             1,042             5,986             3,410
                                                                     --------          --------          --------          --------
   Total interest expense                                               6,482             6,053            19,624            18,798
                                                                     --------          --------          --------          --------

Net interest income                                                     4,359             4,083            13,001            11,524
  Provision for loan losses                                                75                45               200               135
                                                                     --------          --------          --------          --------
Net interest income after  provision for loan losses                    4,284             4,038            12,801            11,389
                                                                     --------          --------          --------          --------

Other income:
  Loan fees and service charges                                           119                63               256               194
  Deposit fees                                                            213               166               531               453
  Gain (loss) on securities available for sale, net                        40                --               216                (5)
  Income from Subsidiary                                                   20                45               135               119
  Gain (loss) on sales of real estate acquired in
  settlement of loans, net                                                (14)               (7)              (36)                4
  Other                                                                    56                31               181               215
                                                                     --------          --------          --------          --------
    Total other income                                                    434               298             1,283               980
                                                                     --------          --------          --------          --------

Operating expenses:
  Compensation and employee benefits                                    1,601             1,352             4,765             4,294
  Occupancy and equipment                                                 262               297               882               900
  Data processing service expense                                         210               193               631               625
  Deposit insurance premiums                                              136               141               407               428
  Other                                                                   630               505             1,655             1,406
                                                                     --------          --------          --------          --------
    Total operating expenses                                            2,839             2,488             8,340             7,653


Income before income tax expense                                        1,879             1,848             5,744             4,716
Income tax expense                                                        695               667             2,125             1,728
                                                                     --------          --------          --------          --------
Net income                                                           $  1,184          $  1,181          $  3,619          $  2,988
                                                                     ========          ========          ========          ========
Basic earnings per share                                             $   0.14          $   0.13          $   0.41          $   0.33
                                                                     ========          ========          ========          ========
Diluted earnings per share                                           $   0.14          $   0.13          $   0.41          $   0.33
                                                                     ========          ========          ========          ========
</TABLE>

        See accompanying notes to the consolidated financial statements.

                                       2

<PAGE>

                            Bayonne Bancshare, Inc.
                                and Subsidiaries
                 Consolidated Statements of Shareholders' Equity
              Nine Month Periods ended December 31, 1998 and 1997
                                 (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                     Common    Additional Unallocated Unamortized Retained      Treasury Accumulated   Total
                                     Stock     Paid in    ESOP        MRP         Earnings      Stock    Other         Stockholders'
                                               Capital    Shares      Shares      Substantially          Comprehensive Equity
                                                                                  Restricted             Loss         
------------------------------------------------------------------------------------------------------------------------------------
<S>                                  <C>       <C>        <C>         <C>         <C>           <C>      <C>           <C>    
Balance at March 31, 1997            $  90     $12,643    $  (598)    $  (378)    $40,658   $    --      $(4,336)      $48,079
Net income for the nine             
month period ended                  
December 31, 1997                       --          --         --          --       2,988        --           --         2,988
Amortization of ESOP                    --         203        163          --          --        --           --           366
Amortization of MRP                     --          72         --         109          --        --           --           181
Dividend Paid                           --          --         --          --        (948)       --           --          (948)
Exercise of stock options               --          61         --          --          --        --           --            61
Comprehensive income                    --          --         --          --          --        --        2,903         2,903
Establishment of second ESOP            --          --     (3,895)         --          --        --           --        (3,895)
Issuance and exchange of            
common stock as a result            
of the conversion/reorganization        --      46,466         --          --          --        --           --        46,466
                                     -----     -------    -------     -------     -------   --------     -------       -------
Balance at December 31, 1997         $  90     $59,445    $(4,330)    $  (269)    $42,698   $    --      $(1,433)      $96,201
                                     -----     -------    -------     -------     -------   --------     -------       -------
                                    
Balance at March 31, 1998            $  91     $60,246    $(4,081)    $  (220)    $43,702   $    --      $(1,089)      $98,649
Net income for the nine                 
month period ended                     
December 31, 1998                       --          --         --          --       3,619        --           --         3,619
Amortization of ESOP                    --         691        358          --          --        --           --         1,049
Amortization of MRP                     --         191         --         371          --        --           --           562
Dividend Paid                           --          --         --          --      (1,657)       --           --        (1,657)
Exercise of stock options                1         224         --          --          --        --           --           225
Purchase of shares for MRP Plan         --          --         --      (3,255)         --        --           --        (3,255)
Purchase of 888,683 shares of
 treasury stock                         --          --         --          --          --   (14,764)          --       (14,764)
Other comprehensive loss                --          --         --          --          --        --       (2,444)       (2,444)
                                     -----     -------    -------     -------     -------  --------      -------       -------
Balance at December 31, 1998         $  92     $61,352    $(3,723)    $(3,104)    $45,664  $(14,764)     $(3,533)      $81,984
                                     -----     -------    -------     -------     -------  --------      -------       -------
</TABLE>                        

        See accompanying notes to the consolidated financial statements.

                                       3

<PAGE>

                    Bayonne Bancshare, Inc. and Subsidiaries

                      Consolidated Statements of Cash Flows
                                 (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                                                    Nine Months Ended December 31,
                                                                          1998          1997
                                                                       ---------     ---------
<S>                                                                    <C>           <C>      
 Cash flows from operating activities:
  Net income                                                           $   3,619     $   2,988

Adjustments to reconcile net income to net cash
provided by (used in) operating activities:

  Depreciation of office properties and equipment                            427           404
  (Gain) loss on securities available for sale                              (216)            5
  Provision for loan losses                                                  200           135
  Loss (gain) on real estate operations                                       36             4
  Amortization of premiums on
   investment securities and mortgage backed securities                    1,882           612
  Amortization of ESOP and MRP shares                                      1,611           747
  Net increase in deferred loan fees                                        (186)         (154)
  Net increase (decrease) in accrued interest receivable                     201          (187)
  Net (decrease) increase in prepaid expenses                               (342)          586
  Net (decrease) increase in other assets                                   (877)         (218)
  Net increase (decrease) in accrued expenses and other liabilities          629        (3,296)
                                                                       ---------     ---------
     Total adjustments                                                     3,365        (1,362)
                                                                       ---------     ---------

    Net cash provided by operating activities                              6,984         1,626
                                                                       ---------     ---------

Cash flows from investing activities:

  Principal payments and maturities on securities
   available for sale                                                    115,740        45,301
  Proceeds from securities available for sale                             94,005            --
  Purchases of securities available for sale                            (185,399)      (93,530)
  Net (increase) decrease in loans receivable                            (60,590)        3,661
  Maturities of securities                                                18,847         1,004
  Proceeds from sales of real estate acquired in
  settlement of loans                                                         25           452
  Purchase of FHLB stock                                                  (3,051)           --
  Purchase of premises and equipment                                        (430)          (29)
                                                                       ---------     ---------
     Net cash used in investing activities                               (20,853)      (43,141)
                                                                       ---------     ---------

  Cash flows from financing activities:
  Net decrease in deposits                                                (3,936)      (21,375)
  Net increase (decrease) in advance payments by borrowers for
   taxes and insurance                                                    (1,222)          397
  Dividends paid                                                          (1,657)         (948)
  Increase in borrowings and repurchase agreements                        29,825         9,950
  Payment on ESOP debt                                                      (163)         (163)
  Purchase of Shares for MRP Plan                                         (3,255)           --
  Treasury stock buy-back repurchase program                             (14,764)           --
  Issuance of common stock as a result of the
  conversion/reorganization                                                   --        42,371
  Exercise of stock options                                                  225            61
                                                                       ---------     ---------
    Net cash provided by financing activities                              5,053        30,293
                                                                       ---------     ---------
</TABLE>

        See accompanying notes to the consolidated financial statements.

                                       4

<PAGE>

                    Bayonne Bancshare, Inc. and Subsidiaries

                      Consolidated Statements of Cash Flows
                                 (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                                                    Nine Months Ended December 31,
                                                                          1998          1997
                                                                       ---------     ---------
<S>                                                                    <C>           <C>      

Net decrease in cash and cash equivalents                                 (8,816)      (11,222)

Cash and cash equivalents at start of period                              16,617        15,472
                                                                       ---------     ---------

Cash and cash equivalents at end of period                             $   7,801     $   4,250
                                                                       =========     =========

Supplemental schedule of cash flow information:

Real estate acquired in settlement of loans                            $     340     $     704
Taxes Paid                                                             $   2,392     $   1,419
Interest Paid                                                          $  19,603     $  15,366
</TABLE>

        See accompanying notes to the consolidated financial statements.

                                       5



<PAGE>

                    BAYONNE BANCSHARES, INC. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1)   Basis of Presentation

     The accompanying unaudited consolidated financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and in conformity with the instructions to Form 10-Q and
Article 10 of Regulation S-X for Bayonne Bancshares, Inc. (the `Company") and
Subsidiaries. The Company is the holding company of First Savings Bank of New
Jersey, SLA, a New Jersey chartered savings and loan association (the "Bank").

2)   Conversion and Reorganization

     On August 22, 1997, Bayonne Bancshares, Inc. in accordance with the Bank's
second-step conversion sold 4,869,190 shares of common stock at a price per
share of $10.00. In addition, each of the 1,410,735 shares of common stock of
First Savings Bank of New Jersey, SLA held by public stockholders were exchanged
for 2.933 shares of common stock of Bayonne Bancshares, Inc. in accordance with
the Bank's Plan of Conversion and Agreement and Plan of Reorganization.

3)   Non-Performing Loans

     Non-performing loans at December 31, 1998, and March 31, 1998 are as
follows (in thousands of dollars):

                                              December 31, 1998   March 31, 1998
                                              -----------------   --------------
Loans delinquent 90 days or more and other
non-performing loans                                $3,371            $3,817
                                                    ======            ======

Loans delinquent 90 days or more and other
non-performing loans as a percentage of loans
receivable, net                                     1.14%              1.62%

     An analysis of the allowance for loan losses for the nine-month periods
ended December 31, 1998 and 1997 is as follows (in thousands of dollars)

                                         December 31, 1998     December 31, 1997
                                         -----------------     -----------------
Balance at start of period                     $2,953               $3,158
Provision charged to operations                   200                  135
Net (charge-offs) recoveries                      (89)                (316)
                                               ------               ------
Balance at end of period                       $3,064               $2,977
                                               ======               ======

                                       6

<PAGE>

4)   Earnings Per Share

     The Company adopted SFAS No. 128, "Earnings Per Share," on December 31,
1997. SFAS No. 128 established the new standard for computation and presentation
of net income per common share. Under the new requirements both basic and
diluted net income per common share are presented. All prior period net income
per common share data has been restated.

     Basic net income per common share is calculated by dividing net income,
less the dividends on preferred stock, if any, by the average common shares
outstanding during the period.

     Diluted net income per common share is calculated similar to that of the
basic net income per common share except that the denominator is increased to
include the number of additional common shares that would have been outstanding
if all potentially dilutive common shares arising from unexercised stock options
were issued during the reporting period.

     As discussed in Note 2, the Company completed a conversion and
reorganization, which included the exchange of previously outstanding shares for
new shares of the stock holding company, Bayonne Bancshares, Inc., at an
exchange ratio of 2.933 to 1. All historical share and per share information has
been adjusted to reflect this change unless otherwise noted.

     The following table summarizes the computation of basic earnings and
diluted earnings per common share for the three and nine months ended December
31, 1998 and 1997:

<TABLE>
<CAPTION>
                                               Three months ended          Nine months ended
                                                   December 31                December 31

(In thousands, except per share data)            1998         1997         1998         1997
                                              ----------   ----------   ----------   ----------
<S>                                               <C>          <C>          <C>          <C>
Earnings available to common shareholders         $1,184       $1,181       $3,619       $2,988
                                              ==========   ==========   ==========   ==========

Weighted average common shares outstanding     8,568,451    8,922,097    8,719,333    8,921,917

Plus common stock equivalents                    130,685      101,754      157,283       99,694

Diluted weighted average shares outstanding    8,699,136    9,023,851    8,876,616    9,021,611

Earnings per common share:

Basic                                              $0.14        $0.13        $0.41        $0.33
                                              ==========   ==========   ==========   ==========

Diluted                                            $0.14        $0.13        $0.41        $0.33
                                              ==========   ==========   ==========   ==========
</TABLE>

                                       7

<PAGE>

5)   Reclassifications

     Certain reclassifications have been made to the 1997 amounts to conform to
the 1998 presentation.

6)   Proposed Merger with Richmond County Financial Corp.

     The Company announced on July 20, 1998 that it had entered into a
definitive agreement to merge with Richmond County Financial Corp., which
agreement was amended and restated on October 14, 1998. Under the terms of the
agreement, which is subject to approval by shareholders of each company and
regulatory authorities, the Company's shareholders will receive 1.05 shares of
Richmond County Financial Corp. common stock for each share of the Company
owned. The transaction is intended to be a tax-free merger accounted for as a
purchase transaction and is expected to be completed by the first quarter of
calendar 1999. The Amended and Restated Agreement and Plan of Merger was
included as an exhibit to the Form 8-K filed by the Company on October 16, 1998.
The merger is expected to be completed in the first calendar quarter of 1999,
subject to regulatory and stockholder approval.

7) Recent Accounting Pronouncement

     In June 1998, the Financial Accounting Standards Board issued SFAS No. 133,
"Accounting for Derivative Instruments and Hedging Activities." This statement
establishes accounting and reporting standards for derivative instruments, and
for hedging activities. This statement is effective for periods commencing
January 1, 2000. The Company is currently evaluating the impact this statement
will have on its results of operations and its financial position. The effect of
adopting this statement is not expected to have a material effect on the
Company's results of operations or financial condition.

8)   Comprehensive Income (Loss)

     The Company has adopted SFAS No. 130, "Reporting Comprehensive Income."
SFAS No. 130 requires the reporting of comprehensive income in addition to net
income from operations. Comprehensive income is a more inclusive financial
reporting methodology that includes disclosure of certain financial information
that historically has not been recognized in the calculation of net income. The
financial statements reflect the adoption of SFAS No 130.

     Total comprehensive income for the nine months ended December 31, 1998 and
1997 was $1,175,000 and $5,891,000 respectively. For the nine months ended
December 31, 1998, total comprehensive income represented net income of
$3,619,000 and other comprehensive loss of $2,444,000. For the nine months
ended December 31, 1997,

                                       8


<PAGE>

total comprehensive loss represented net income of $2,988,000 and other
comprehensive income of $2,903,000. Other comprehensive income for the
above-mentioned periods related to unrealized gains/losses on securities
available for sale, net of tax.

Item 2. Management's Discussion and Analysis of Financial Condition and
        Results of Operations

Financial Condition

     Stockholders' equity decreased by $16.6 million to $82.0 million at
December 31, 1998 from $98.6 million at March 31, 1998. The decrease in
stockholders' equity was primarily attributable to the purchase of 888,683
shares of Bayonne Bancshares, Inc. stock, totaling $14.8 million, as shares
purchased by the Company in the open market pursuant to its stock repurchase
program and shares purchased in the open market to fund stock awards under the
Company's stock-based incentive plan were partially offset by net income of $3.6
million for the nine months ended December 31, 1998. At December 31, 1998, the
Bank's tangible, core and risk based capital ratios were 9.99%, 9.99%, and
23.22%, respectively.

     Total assets increased by $8.4 million to $654.5 million at December 31,
1998 compared to $646.1 million at March 31, 1998. Securities available for sale
decreased by $48.7 million or 13.4% to $314.1 million at December 31, 1998 from
$362.8 million at March 31, 1998. The decrease was primarily attributable to the
sale of $45.0 million of U.S. Government Agency securities and $12.0 million of
mortgage backed securities which was partially offset by the purchase of $38.0
million of variable and fixed rate trust preferred securities.

     Loans receivable, net increased by $60.3 million or 25.6% to $295.8 million
at December 31, 1998 compared to $235.5 million at March 31, 1998. The increase
resulted primarily from the purchase of $80 million of seasoned, fixed rate
single family loans partially offset by net amortization and payoffs of $49.8
million on mortgage loans during the nine month period.

     Total liabilities increased by $25.1 million or 4.6% to $572.5 million as
of December 31, 1998 compared to $547.4 million at March 31, 1998. Borrowings
increased by $29.8 million or 25.9% to $144.8 million at December 31, 1998
compared to $115.0 million at March 31, 1998. Borrowings were used to increase
the Company holdings of trust preferred issues and mortgage backed securities
and to fund a portion of the whole loan purchase and the outflow of maturing
high yielding certificates of deposit.

Results of Operations for the Three Months Ended December 31, 1998

     Net income was $1.2 million for the three months ended December 31, 1998
compared to $1.2 million for the quarter ended December 31, 1997. Total interest
and dividend income increased by $705,000 or 7.0% to $10.8 million for the three
months ended December 31,

                                       9

<PAGE>

1998 from $10.1 million for the three months ended December 31, 1997. This
increase resulted primarily from an increase in average interest earning assets
of $55.8 million or 9.5% to $642.9 million for the three months ended December
31, 1998 from $587.1 million for the three months ended December 31, 1997,
partially offset by a decrease in the yield on average interest earning assets
to 6.74% for the three months ended December 31, 1998, compared to 6.86% for the
three months ended December 31, 1997. The increase in average interest earning
assets was primarily due to the $80 million in whole loans purchased on June 30,
1998.

     Total interest expense increased by $429,000 or 7.1% to $6.5 million for
the three months ended December 31, 1998 compared to $6.1 million for the three
months ended December 31, 1997. The increase resulted primarily from an increase
in average interest bearing liabilities of $60.6 million or 12.0% to $563.9
million for the three months ended December 31, 1998 compared to $503.3 million
for the three months ended December 31, 1997, partially offset by a decrease in
the yield on average interest bearing liabilities to 4.60% for the three months
ended December 31, 1998 from 4.81% for the three months ended December 31, 1997.
Average wholesale borrowings increased by $69.3 million or 92.9% to $143.9
million for the three months ended December 31, 1998 compared to $74.6 million
for the comparable prior year period.

     The provision for loan losses totaled $75,000 and $45,000 for the
three-month period ended December 31, 1998 and 1997 respectively. The provision
is a result of management's judgement based on a review of it's loans and
consideration of a variety of factors including, but not limited to, (1) the
risk characteristics of its loan portfolio, (2) current economic conditions, (3)
actual losses previously experienced and (4) the existing levels of reserve for
possible losses in the future. Non-performing loans at December 31, 1998 and
March 31, 1998 were $3.4 million and $3.8 million or 1.14% and 1.62% of loans
receivable, net, respectively.

     Total other income increased by $136,000 or 45.6% to $434,000 for the three
months ended December 31, 1998 compared to $298,000 for the three months ended
December 31, 1997. The increase in total other income resulted primarily from
increased fees on deposit accounts of $47,000 to $213,000 for the three months
ended December 31, 1998 from $166,000 for the same prior year period, and gains
on sales of securities available for sale of $40,000.

     Total operating expenses increased by $351,000 or 14.1% to $2.8 million for
the three months ended December 31, 1998 compared to $2.5 million for the three
months ended December 31, 1997. The increase for the three month period was due
primarily to an increase of $249,000 in compensation and employee benefits
relating to the stock-based incentive plan and ESOP expenses of $259,000,
partially offset by a $36,000 decrease in compensation and employee benefits on
lower executive salary expense.

     Income tax expense for the quarter increased by $28,000 to $695,000 for the
three months ended December 31, 1998 compared to $667,000 for the comparable
prior year

                                       10

<PAGE>

quarter. The effective tax rates for the quarters ended December 31, 1998 and
1997 were 37.0% and 36.1%, respectively.

Results of Operations for the Nine Months Ended December 31, 1998

     Net income increased by $631,000 or 21.0% to $3.6 million for the nine
months ended December 31, 1998 compared to $3.0 million for the nine months
ended December 31, 1997. This increase resulted primarily from an increase in
average interest earning assets of $68.8 million or 11.9% to $647.9 million for
the nine months ended December 31, 1998 compared to $579.1 million for the nine
months ended December 31, 1997, partially offset by a decrease in the yield on
average interest earning assets to 6.71% for the nine months ended December 31,
1998 compared to 6.97% for the nine months ended December 31, 1997. The increase
in average interest earning assets was primarily due to the $80.0 million in
whole loans purchased on June 30, 1998.

     Total interest expense increased by $826,000 or 4.4% to $19.6 million for
the nine months ended December 31, 1998 compared to $18.8 million for the nine
months ended December 31, 1997. This increase resulted primarily from an
increase of $46.5 million or 9.0% in average interest bearing liabilities to
$564.5 million for the nine months ended December 31, 1998 from $518.0 million
for the nine months ended December 31, 1997 partially offset by a decrease in
the yield on average interest bearing liabilities to 4.63% for the nine months
ended December 31, 1998 from 4.84% for the nine months ended December 31, 1997.
Average wholesale borrowings increased by $61.7 million or 75.8% to $143.1
million for the nine months ended December 31, 1998 compared with $81.4 million
for the comparable prior year period.

     The provision for loan losses totaled $200,000 and $135,000 for the
nine-month periods ended December 31, 1998 and 1997 respectively. The provision
is the result of management's judgement based on a review of its loans and a
consideration of a variety of factors including, but not limited to, (1) the
risk characteristics of its loan portfolio, (2) current economic conditions, (3)
actual losses previously experienced and (4) the existing levels of reserve for
possible loan losses in the future. Non-performing loans at December 31, 1998
and March 31, 1998 were $3.4 million and $3.8 million or 1.14% and 1.62% of
loans, net, respectively.

     Total other income increased by $303,000 or 30.9% to $1.3 million for the
nine months ended December 31, 1998 compared to $1.0 million for the nine months
ended December 31, 1997. The increase resulted primarily from an increase in
gains on sales of securities available for sale of $221,000 to $216,000 for the
nine months ended December 31, 1998 from a loss of $5,000 for the prior nine
month time period, and increased fees on deposit accounts of $78,000 for the
comparable nine month time periods.

                                       11

<PAGE>

     Total operating expenses increased by $687,000 or 9.0% to $8.3 million for
the nine months ended December 31, 1998 compared to $7.6 million for the nine
months ended December 31, 1997. The increase for the nine months ended December
31, 1998 was primarily due to a $471,000 increase in compensation and employee
benefit expense, as the stock-based incentive plan and ESOP expenses increased
by $810,000 and were partially offset by lower salaries and employee benefits of
$378,000 relating to lower executive salary expense.

     Income tax expense increased to $2.1 million for the nine months ended
December 31, 1998 from $1.7 million for the nine months ended December 31, 1997
as a result of an increase of $1.0 million in pre-tax income for the nine month
period ended December 31, 1998.

Capital

     The Office of Thrift Supervision ("OTS") equires that the Bank meet minimum
tangible, core and risk-based capital requirements. As of December 31, 1998, the
Bank exceeded all regulatory capital requirements. The Bank's required, actual
and excess capital levels as of December 31, 1998 were as follows (in thousands
of dollars):

<TABLE>
<CAPTION>
                                                                                                                    Excess of Actual
                                         Required             % of              Actual               % of           Over Regulatory
                                          Amount             Assets             Amount              Assets           Requirements
                                          ------             ------             ------              ------           ------------
<S>                                       <C>                 <C>               <C>                  <C>               <C>
Tangible Capital ..................       $ 9,587             1.50%             $63,854              9.99%             $54,267
Core Capital ......................       $25,565             4.00%             $63,854              9.99%             $38,289
Risk-based Capital ................       $23,053             8.00%             $63,854             22.16%             $40,801
</TABLE>

     If the allowance for marketable debt and equity securities were included in
capital, the Bank's tangible, core and risk-based capital ratios would be 9.76%,
9.76% and 21.59% respectively, at December 31, 1998.

Liquidity

     The Bank is required to maintain minimum levels of liquid assets as defined
by OTS regulations. This requirement, which varies from time to time depending
upon economic conditions and deposit flows, is based upon a percentage of
deposits and short-term borrowings. The required ratio currently is 5.0%. The
Bank's liquidity ratio averaged 16.05% during the month of December 31, 1998 and
18.42% during three months ended December 31, 1998. The Bank adjusts liquidity
as appropriate to meet its asset and liability management objectives.

Year 2000 Compliance

     The Company and the Bank rely on computers for the daily conduct of their
business and for data processing. There is concern among industry experts that
on

                                       12

<PAGE>

January 1, 2000 computers will be unable to "read" the Year 2000 and there may
be widespread computer malfunctions. The Bank recognized that a comprehensive
and coordinated plan of action was needed to ensure readiness to perform Year
2000 processing. A Year 2000 Committee has been formed to implement the Year
2000 project, develop policies, document readiness of the Bank and the Company
to accommodate Year 2000 processing, and track and test progress towards full
compliance. The Bank contracts with a service bureau (the "service provider") to
provide the majority of its data processing and is dependent upon purchased
application software. In house applications are limited to word-processing and
spreadsheet functions.

Risk of Year 2000 Issues

     To date, the Company has not identified any system which presents a
material risk of failing to be Year 2000 compliant in a timely manner, or for
which a suitable alternative cannot be implemented. However, as the Company
progresses with its Year 2000 transition, systems or equipment may be identified
which present a material risk of business interruption. Such disruption may
include the inability to process customer accounting transactions, including
deposits, withdrawals, loan payments and disbursements; the inability to
reconcile and record daily activity, the inability to process loan applications
or the track delinquencies; the inability to generate checks or to clear funds.
In addition, if any of the Company's major borrowers should fail to achieve Year
2000 compliance, and should they experience a disruption of their own
businesses, their ability to meet their obligations to the Company may be
seriously impaired.

State of Readiness

     The Company's subsidiary, the Bank, is in the process of ensuring that its
external vendors and its data processing service provider are adequately
addressing the system and software issues related to the Year 2000 by obtaining
written system certifications that the systems are fully Year 2000 compliant or
that the vendor has a plan to become fully compliant by December 31, 1999. The
Bank has contacted 21 of its significant vendors and service providers and to
date has received certification from 67% of the vendors and service providers
that they are Year 2000 compliant. The Bank will utilize the primary servicers,
end-to-end tests, to simulate daily processing on sensitive century change
dates. In the evaluation, the Bank will ensure that critical operations will
continue if servicers or vendors are unable to achieve the Year 2000
requirements.

     The Bank has contacted 55 major borrowers to survey their Year 2000
readiness in order to anticipate any potential exposure. The Bank considers a
major borrower to be one who has a business from which the repayment of the loan
will be derived and for which the Year 2000 readiness therefore is an issue. The
value of loans of which borrowers were surveyed totaled $2.2 million and
represents 100% of the Bank's major borrowers. The Bank has not contacted its
largest dollar deposit customers to determine their readiness for Year 2000.

                                       13

<PAGE>

     The Company does not anticipate that there will be any significant or
material condition which will impact ability to deliver accurate data processing
services before, during and after the transition to the new millennium,
therefore no formal contingency plans exist at this time. However, results of
system tests conducted by the Company and by other users of the service provider
will be carefully monitored to ensure that all issues have been identified and
successfully remediated.

     The Company believes it has developed an effective plan to address the Year
2000 problem and that, based on the available information, its Year 2000
transition will not have a material effect on its business, operations or
financial results. However, the Company has no control over the progress of
third parties in addressing their own Year 2000 issues. If the necessary changes
are not effected or are not completed in a timely manner, or if unanticipated
problems arise, there may be a material impact on the Company's financial
condition and results of operations.

     The Committee has completed a systems inventory and obtained certification
from the service provider. The Committee has identified critical applications
and implemented hardware system upgrades and system replacements as of December
31, 1998. All upgrades have been implemented and will be substantially tested
for the Year 2000 compliance by the first quarter of 1999.

Cost to Address the Company's Year 2000 Issues

     The Company's costs to achieve Year 2000 compliance are not expected to
have a material financial impact on the Company. The Company intends to fund
such costs from its current operations. However, as stated above, there can be
no assurance that all such costs have been identified, or that there may not be
some unforeseen cost which may have a material adverse effect on the Company's
financial condition and results of operations. The Company has budgeted $250,000
for hardware system upgrades and system replacements, which has been approved by
the Board of Directors.

Contingency Plans

     The Company is in the process of developing two types of contingency plans.
The remediation plan will identify components of mission critical applications
which are judged, at some point prior to December 31, 1999, to be at risk of
failure to achieve complete renovation, validation and implementation. Business
interruption plans will ensure that the Company has sufficiently planned for
unanticipated system failures at critical production dates before, on and after
January 1, 2000. The Company expects to have its contingency plans completed by
June 30, 1999.

Remediation Plan

     The Company is in the process of developing a remediation plan with the
primary servicer. The plan will identify components of applications which are
judged, at some

                                       14

<PAGE>

point prior to December 31, 1999, to be at risk of failure to achieve complete
renovation, validation and implementation. The Remediation Plan will ensure that
the company has sufficiently planned for unanticipated system failures at
critical production dates before, on and after January 1, 2000.

Business Interruption Plan

     These plans would be invoked if unanticipated Year 2000 problems occur in
production, similar to disaster recovery plans. Essentially, they require that
resources are planned for deployment to ensure that such an interruption does
not threaten the viability of the Company. The Company will review and modify
its current business interruption plan, with its primary servicer, to
specifically address the special circumstances of a disruption due to a Year
2000 related component failure.

Item 3. Quantitative and Qualitative Disclosures About Market Risk

     There have been no material changes in information regarding quantitative
and qualitative disclosures about market risk as of December 31, 1998 from the
information as of March 31, 1998, which was disclosed in the Company's 1998
Form 10-KA.

PART II. OTHER INFORMATION

Legal Proceedings

     In the normal course of business, the Company may be a party to various
outstanding legal proceedings and claims. In the opinion of management, the
financial position of the Company will not be materially affected by the outcome
of such legal proceedings and claims.

Changes in Securities

     Not applicable.

Defaults upon Senior Securities

     Not applicable.

Submission of Matters to Vote of Security Holders

     None.

Other Information

The Company announced on July 20, 1998 that it had entered into a definitive
agreement to merge with Richmond County Financial Corp., which agreement was
amended and restated on October 14, 1998. Under the terms of the agreement,
which is subject to

                                       15

<PAGE>

approval by shareholders of each company and regulatory authorities, the
Company's shareholders will receive 1.05 shares of Richmond County Financial
Corp. common stock for each share of the Company owned. The transaction is
intended to be a tax-free merger accounted for as a purchase transaction and is
expected to be completed by the first quarter of calendar 1999. The Amended and
Restated Agreement and Plan of Merger was included as an exhibit to the Form 8-K
filed by the Company on October 16, 1998.

Exhibits and Reports on Form 8-K

(a)  The following exhibits are filed as part of this report:

     3.1  Certificate of Incorporation of Bayonne Bancshares, Inc.*

     3.2  Bylaws of Bayonne Bancshares, Inc.*

     4.0  Stock Certificate of Bayonne Bancshares, Inc.*

     11.0 Computation of earnings per share (filed herewith)

     27.0 Financial Data Schedule (filed herewith)

(b)  A report on Form 8-K was filed on July 27, 1998 for the Agreement and Plan
     of Merger with Richmond County Financial Corp. The Company also filed a
     Form 8-K on October 16, 1998 to disclose the amendment and restatement of
     the Agreement and Plan of Merger

*Incorporated herein by reference in this document from the Exhibits to the Form
S-1 Registration Statement, filed on March 13, 1997, and any amendments thereto
(Registration No. 333-23199).

                                       16

<PAGE>

                                   SIGNATURES

     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.

                                           BAYONNE BANCSHARES, INC.

Date: February 12, 1999               By:
                                         ---------------------------------------
                                      Michael A. Nilan
                                      President and Chief Executive Officer


Date: February 12, 1999               By:
                                         ---------------------------------------
                                      Eugene V. Malinowski
                                      Vice President and Chief Financial Officer



                                       17