  We formulate and solve a model of two planes of antiferromagnetically
correlated electrons coupled together by a weak antiferromagnetic interaction
of strength $\lambda$. We show that in-plane antiferromagnetic correlations
dramatically enhance the pairing effect of the interplane interaction. For the
case where the in-plane correlation length $\kappa^{-1} \sim T^{-1/2}$, we find
that the interaction $\lambda$ leads to spin pairing at a temperature $T^{*}
\sim \lambda$, much higher than the usual BCS result $exp(-J/\lambda)$. We
suggest that this is a possible explanation of the spin gap effects observed
below $T^{*} \sim 150K$ in $YBa_2Cu_3O_{6.6}$.

Condensed Matter