  Let $G = \ZZ_p$, $p$ an odd prime, act freely on a finite-dimensional
CW-complex $X$ with mod $p$ cohomology isomorphic to that of a lens space
$L^{2m-1} (p;q_1,...,q_m)$. In this paper, we determine the mod $p$ cohomology
ring of the orbit space $X/G$, when $p^2\nmid m$.
