The semiempirical MO method 'HAM/3' developed by Lindholm and coworkers about two decades ago has been known to have a deficiency that it gives split energies for the degenerate eigenstates. We have recently proposed a group-theoretical way to remedy the internally broken symmetry of the HAM/3 Hamiltonians [JCPE J. 11 (1999) 161]. In this paper we describe the proposed scheme explicitly and present some results of its application to various small symmetric molecules. It is demonstrated that the proposed scheme gives correct degeneracies for molecules with symmetry like D6h, D2d, and Dinfinityh. An error found in a subroutine of the original HAM/3 program for calculating triplet states has been also corrected. The corrected and modified version of HAM/3 may now be used as an independent semiempirical MO method for spectroscopic purposes in addition to CNDO/S or INDO/S. (C) 2002 Elsevier Science B.V. All rights reserved.61841671147154