  It is shown that in the Schwarzschild background there exists direct
counterpart of the Ba\~{n}ados-Silk-West effect for spinning particles. This
means that if two particles collide near the black hole horizon, their energy
in the centre of mass frame can grow unbounded. In doing so, the crucial role
is played by so-called near-critical trajectories when particle's parameters
are almost fine-tuned. Direct scenario of the collision under discussion is
possible with restriction on the energy-to-mass ratio \thinspace
$E/m<\frac{1}{2\sqrt{3}}$ only. However, if one takes into account multiple
scattering, this becomes possible for $E\geq m$ as well.
