  We constructed Hirota-Kimura type discretization of the classical
nonholonomic Suslov problem of motion of rigid body fixed at a point. We found
a first integral proving integrability. Also, we have shown that discrete
trajectories asymptotically tend to a line of discrete analogies of so-called
steady-state rotations. The last property completely corresponds to well-known
property of the continuous Suslov case. The explicite formulae for solutions
are given. In n-dimensional case we give discrete equations.
