<PAGE>   1
                                  UNITED STATES 
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                   FORM 10-K/A

[X]      ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

         For the fiscal year ended DECEMBER 31, 1996
                                   -----------------

[ ]      TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

         For the transition period from             to
                                        ------------   -------------

         Commission File Number 0-19431
                                -------

                            ROYAL APPLIANCE MFG. CO.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

              Ohio                                            34-1350353
--------------------------------------------------------------------------------
(State or other jurisdiction of                 (I.R.S. Employer Identification)
incorporation or organization)

650 Alpha Drive, Cleveland, Ohio                                44143
--------------------------------------------------------------------------------
(Address of principal executive offices)                      (Zip Code)

                                 (216) 449-6150
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)

Securities Registered Pursuant to Section 12(b) of the Act:

Common Shares, Without Par Value               New York Stock Exchange
--------------------------------------------------------------------------------
     (Title of Each Class)           (Name of Each Exchange on which Registered)

Securities Registered Pursuant to Section 12(g) of the Act:  None



                                        1

<PAGE>   2



PART IV

ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON FORM 8-K
-------   ----------------------------------------------------------------


        EXHIBITS
        --------

        Form 10K for December 31, 1996, is amended by the substitution of the
        amended Form 11K, with respect to the Royal Appliance Mfg. Co. Employees
        Profit Sharing Retirement Plan and Trust.


           99.1  Form 11-K Annual Report for Royal Appliance Mfg. Co. Employees
                 Profit Sharing Retirement Plan and Trust.





                                   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, on this 24th day of
February, 1998.

                           ROYAL APPLIANCE MFG. CO.
                                 Registrant

                           By   /s/ Richard G Vasek
                              ----------------------------------
                                               Richard G. Vasek
                                Controller, Secretary & Chief Accounting Officer
                                        (Principal Accounting Officer)

                           Date February 24, 1998
                                --------------------------------


                                        2