  We present the results of a numerical calculation of the $B\to K^* \gamma$
form factors. The results have been obtained by studying the relevant
correlation functions at $\beta=6.0$, on an $18^3 \times 64$ lattice, using the
${\rm O(a)}$-improved fermion action, in the quenched approximation. From the
study of the matrix element $<K^*| \bar s \sigma_{\mu\nu} b | B>$ we have
obtained the form factor $T_1(0)$ which controls the exclusive decay rate. The
results are compared with the recent results from CLEO. We also discuss the
compatibility between the scaling laws predicted by the Heavy Quark Effective
Theory (HQET) and pole dominance, by studying the mass- and $q^2$-dependence of
the form factors. From our analysis, it appears that the form factors follow a
mass behaviour compatible with the predictions of the HQET and that the
$q^2$-dependence of $T_2$ is weaker than would be predicted by pole dominance.
