Let G = Z2 act freely on a finitistic space X. If the mod 2 cohomology of X
is isomorphic to the real projective space RP2n+1(resp. complex projective
space CP2n+1) then the mod 2 cohomology of orbit spaces of these free actions
are RP1 xCPn(resp. RP2xHPn) [11]. In this paper, we have discussed converse of
this result. We have showed that if the mod 2 cohomology of the orbit space X/G
is RP1xCPn(resp. RP2 x HPn). Similar, results for p > 2, a prime, is also
discussed. It is proved that one of the possibilities of orbit spaces of free
involutions on product of projective spaces RPn x RP2m+1(resp. CPn x CP2m+1) is
RP1 x RPn x CPm(resp. RP2 x CPn x HPm) [12]. The converse of these statements
are also discussed