  By a canonical transformation of the three-band Hubbard model, we introduce
an effective Hamiltonian for the propagation of two holes doped into the ground
state of the Cu-O plane. When the pair belongs to the $^{1}B_{2}$ or $%
^{1}A_{2}$ Irreducible Representations of the C$_{4v}$ Group, the bare holes do
not interact by the on-site repulsion; the effective interaction between the
dressed holes is obtained analytically in terms of renormalized matrix
elements, and generalizes earlier findings from cluster calculations. The Fermi
liquid is unstable and numerical estimates with reasonable parameters of the
binding energy of the pair are in the range of tens of meV. Our scheme
naturally lends itself to embody phonon-mediated and other interactions which
cannot occur in the Hubbard model but may give important contributions.
