  We continue our study of the IIB matrix model on fuzzy $S^2 \times S^2$.
Especially in this paper we focus on the case where the size of one of
$S^2\times S^2$ is different from the other. By the power counting and SUSY
cancellation arguments, we can identify the 't Hooft coupling and large $N$
scaling behavior of the effective action to all orders. We conclude that the
most symmetric $S^2 \times S^2$ configuration where the both $S^2$s are of the
same size is favored at the two loop level. In addition we develop a new
approach to evaluate the amplitudes on fuzzy $S^2 \times S^2$.
