  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
(LCSR). 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. We present results for the corresponding branching ratios and
compare them with the existing theoretical predictions.
