  Critical temperature reduction $\Delta T_c$ is considered for a thin film of
a layered superconductor (S) with a rough surface covered by a thick layer of a
normal metal (N). The roughness of the SN interface increases the penetration
of electrons from the normal metal into the superconductor and leads to an
enhancement of the proximity effect. The value of $\Delta T_c$ induced by the
roughness of the SN interface can be much higher than $\Delta T_c$ for a film
with a plain surface for an extremely anisotropic layered superconductor with
the coherence lengths $\xi_a,\xi_b\gg\xi_c$.
