  The exclusive rare radiative B meson decays to orbitally excited axial-vector
mesons K_1^*(1270), K_1(1400) and to the tensor meson K_2^*(1430) are
investigated in the framework of the relativistic quark model based on the
quasipotential approach in quantum field theory. These decays are considered
without employing the heavy quark expansion for the s quark. Instead the s
quark is treated to be light and the expansion in inverse powers of the large
recoil momentum of the final K^{**} meson is used to simplify calculations. It
is found that the ratio of the branching fractions of rare radiative B decays
to axial vector K^*_1(1270) and K_1(1400) mesons is significantly influenced by
relativistic effects. The obtained results for B decays to the tensor meson
K_2^*(1430) agree with recent experimental data from CLEO.
