The paper presents a group-theoretical analysis of the new approach to calculating molecular ions C-60(N+/-) (I-h) based on the multipole expansion of interelectronic interactions and of the results of calculations presented by Nikolaev and Michel (NM) [J. Chem. Phys. 117, 4761 (2002)]. By combining the NM method with the theory of "integral invariants" developed by Plakhutin and Judd & Lo, we represent the basic formulas and quantities of the former method in the symmetry-reduced form corresponding to a full separation of variables. This enables us to derive two general relationships between multipole expansion data for complementary configurations, electronic gamma(N) and hole (gamma(+))(N). These relationships are used to correct the numerical data (coefficients of the multipole expansion and the energies of the states) presented by NM for the hole configurations (t(1u)(+))(N) and (h(u)(+))(N). Some new possible applications of the modified (symmetry-reduced) NM method are discussed. (C) 2003 American Institute of Physics.