  The canonical transformation diagonalizing the one-particle tight binding
Hamiltonian for an alternating chain with two non-equivalent sites per unit
cell has been used to introduce the Hubbard-like interactions (on-site,
inter-site, bond-site and intra-bond) in the corresponding two-band model. The
considerations have been restricted to the particular case, suggested by the
undistorted 3/4-filled $CuO_{3}$ chain, where the alternating structure comes
only from non-equal on-site atomic energies and the gap between the two bands
is sufficiently large. The renormalization group method has been then applied
to the upper band of this model and the corresponding phase diagram has been
analyzed in terms of some renormalized (density dependent) Hubbard-type
couplings for arbitrary filling of the upper band. The particular case of
$CuO_{3}$ chain is also discussed and the corresponding phase diagram has been
drawn in terms of the original (and realistic) coupling constants.
