  Using the QCD sum rules approach and the complete leading--logarithmic
short--distance coefficients determining the penguin--amplitude, we obtain
$B(B\to K^*\gamma) = (6.8\pm 2.4)\cdot 10^{-5}$ for top--quark masses in the
range (150--200) GeV and $|V_{cb}| = 0.035$ for $\tau_B = 1.5\,\text{ps}$. The
ratio to the inclusive rate is $B(B\to K^*\gamma)/B(B\to X_s\gamma) = (20\pm
6)\% $.
