  We calculate the effective interaction $W_{eff}$ between two holes added to
the ground state of the repulsive three-band Hubbard model. To make contact
with Cooper theory and with earlier Hubbard model cluster studies, we first use
a perturbative canonical transformation, to generate a two-body Hamiltonian.
Then, we extend the results to all orders. The approach is exact in principle,
and we obtain a close analytic expression including explicitly the effects of
all virtual transitions to 4-body intermediate states. Our scheme naturally
lends itself to embody off-site, inter-planar, phonon-mediated and other
interactions which are not considered in the Hubbard model but may well be
important. The result depends qualitatively on the symmetry of the two-hole
state: $^{1}B_{2}$ and $ ^{1}A_{2}$ pairs are special, because the bare holes
do not interact by the on-site repulsion (W=0 pairs). The effective interaction
in these channels is attractive and leads to a Cooper-like instability of the
Fermi liquid; however $W_{eff}$ is repulsive for Triplet pairs. Bound two-hole
states of the same nature were reported earlier in small cluster calculations
by exact diagonalisation methods; only symmetric clusters are good models of
the plane. Once $W_{eff}$ is known, the pair eigenfunction is determined by an
integral equation. We present numerical estimates of the binding energy
$|\Delta|$ of the pairs, which is in the physically interesting range of tens
of meV if unscreened on-site repulsion parameters are used.
