  We give a more complete calculation of $b \to s e^+e^- $ decay including
leading log QCD corrections from $m_{top}$ to $M_W$ in addition to corrections
from $M_{W}$ to $m_b$. The differential decay rate is found to be slightly
suppressed for a large invariant mass of the $e^+e^- $ pair; while the
integrated width is slightly enhanced comparing with the results without the
QCD running from $m_{top}$ to $M_W$.
