  The renormalization effects from the b-quark scale down to the
non-perturbative QCD regime are studied for rare $B$-decays at the heavy
b-quark limit. Phenomenological consequences of these effects are investigated.
We find that the anomalous scaling behavior plays a positive role in making
non-perturbative model calculations consistent with recent CLEO measurements of
$B\rightarrow K^* \gamma .$
