We have demonstrated that an SU(2)(qL) x SU(2)(IL) x U(1)y model including S-3 x Z(4) discrete symmetry and appropriate Higgs fields gives rise to almost degenerate Majorona neutrino masses of (1-3) eV through the usual see-saw mechanism due to the introduction of an intermediate mass scale at which lepton number violation occurs. We have considered two different types of discrete symmetry transformations (Type A and Type B). The hierarchy of neutrino mass obtained due to the Type A transformation reconciles with the solar and atmospheric neutrino deficits whereas the Type B transformation generates an inverted mass hierarchy of neutrinos which explains the solar and the LSND experimental results. (C) 1997 Elsevier Science B.V.