At finite Reynolds numbers, particles migrate across flow streamlines to their equilibrium positions in microchannels. Such a migration is attributed to an inertial lift force, and it is well known that the equilibrium location of neutrally buoyant particles is determined only by their size and the Reynolds number. Here we demonstrate that the decoration of a bottom wall of the channel by superhydrophobic grooves provides additional possibilities for manipulation of neutrally buoyant particles. It is shown that the effective anisotropic hydrodynamic slip of such a bottom wall can be readily used to alter the equilibrium positions of particles and to generate their motion transverse to the pressure gradient. These results may guide the design of novel inertial microfluidic devices for efficient sorting of neutrally buoyant microparticles by their size.