  We predict contributions of higher $K$-resonances to the radiative rare
decays $b\to s\gamma$, in the framework of the QCD sum rules on the light cone,
which combines the traditional QCD sum rule method with the description of
final state mesons in terms of the light-cone wave functions of increasing
twist. Our calculations are restricted to the leading twist-two operators for
$K^*(892)$ and to the asymptotic wave function for the other $K^{**}$-mesons.
  Using experimental data on the semileptonic $\tau\to K^{**}\nu_{\tau}$
decays, we extract the corresponding decay constants for vector and
axial-vector $K^{**}$-mesons. Based on our estimate of the transition form
factor $F_1^{K^*(892)}(0)=0.32 \pm 0.06$ and the $K_2^*(1430)$ decay constant
$f_{K_2^*(1430)}=(160\pm 20) MeV$, we find good agreement with experimental
results. The two largest fractions of the inclusive $b\to s\gamma$ branching
ratio are found to be $(10.0\pm 4.0)%$ for $B\to K^*(892) \gamma$ and $(5.0\pm
2.0)%$ for $B\to K_2^*(1430)\gamma$ decays. We also compare our results with
the existing theoretical predictions.
