  Our article is devoted to the study of the rare $B\to K^\ast
\ell^+\ell^-$~decay where $\ell=e,\mu,\tau$. We compute the relevant form
factors in the framework of the covariant quark model with infrared confinement
in the full kinematical momentum transfer region. The calculated form factors
are used to evaluate branching fractions and polarization observables in the
cascade decay $B\to K^\ast(\to K\pi)\ell^+\ell^-$. We compare the obtained
results with available experimental data and the results from other theoretical
approaches.
