  A derivation of the t-J model of a highly-correlated solid is given starting
from the general many-electron Hamiltonian with account of the
non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands
(i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is
demonstrated. The non-orthogonality corrections are shown to lead to occurrence
of indirect antiferromagnetic exchange interaction even in the limit of the
infinite on-site Coulomb repulsion. Consequences of this treatment for the
magnetism formation in narrow energy bands are discussed. Peculiarities of the
case of ``frustrated'' lattices, which contain triangles of nearest neighbors,
are considered.
