A modified version of the tight-binding method of band-structure calculations, based on well-defined localized orbitals, is proposed. The localized orbitals are obtained as the self-consistent eigenstates of a local Hamiltonian defined in a unit cell at each atomic site, with an arbitrary localizing potential about each cell. The crystal eigenstates are computed by expanding the Bloch functions in localized orbitals and diagonalizing a crystal Hamiltonian which compensates for the arbitrary localizing potential. A general discussion of this method and a comparison with similar approaches is given. Specific results are reported and discussed for the case of NiO. © 1981 The American Physical Society.