  One-loop divergences appearing in the entropy of a quantum black hole are
proven to be completely eliminated by the standard renormalization of both the
gravitational constant and other coefficients by the $R^2$-terms in the
effective gravitational action. The essential point of the proof is that due to
the higher order curvature terms the entropy differs from the
Bekenstein-Hawking one in the Einstein gravity by the contributions depending
on the internal and external geometry of the horizon surface.
