The variational scheme of Gutzwiller has been reexamined so as to apply it to the case of degenerate narrow bands. The ground-state wave function for electrons is investigated for an arbitrary density of electrons and an arbitrary strength of interaction. The typical features of a metal, particularly the Fermi surface, are preserved in this approach as opposed to some other methods. The Coulomb repulsion among electrons scatters the electrons from below to above the Fermi surface of uncorrelated bands. Under the assumption that only the intra-atomic Coulomb interaction is important, the probability of electrons being scattered is larger for the paramagnetic state than for the ferromagnetic state. Therefore the ferromagnetic ground state is favored if the density of states is large at the band edges. The degenerate-band-model Hamiltonian is spin dependent, hence the results obtained from it do not have to obey the theorem of Lieb and Mattis. © 1971 The American Physical Society.