Supersymmetric predictions for the inclusive $b\to s\gamma$ decay

We study the penguin induced transition $b\to s\ \gamma$ in the minimal N=1 supersymmetric extension of the Standard Model with radiative breaking of the electroweak group. We include the effects of one-loop corrections to the Higgs potential and scalar masses. We show that the present upper and lower experimental limits on the inclusive decay sharply constrain the parameter space of the model in a wide range of $\tan\beta$ values. The implications of the recently advocated relation $|B|\ge 2$ for the bilinear SUSY soft breaking parameter in grand unified theories are also analyzed.