  We investigate the rare production of the pair of $S-$ and $P-$ wave
$B_c$-meson in the Higgs boson decay in the perturbative Standard Model and
relativistic quark model. Relativistic amplitudes and decay widths are
constructed with the account of the relative motion of heavy quarks forming
$B_c$ mesons. When constructing the Higgs boson decay amplitudes, the method of
projection operators on the $S-$ and $P-$wave states of quarks is used.
Relativistic corrections are expressed in terms of special relativistic
parameters and are calculated numerically in the quark model. The dependence of
the decay widths of the Higgs boson on various sources of relativistic
corrections is investigated.
