A ring R is said to be an ring if a right (left) R-module is finitely generated if and only if it is reflexive as right (left) R-module. A quasi-Frobenius ring is an artinian cogenerator ring. In [10],the authors showed in particular, that a ring is a quasi-Frobenius Duo-ring if and only if it is an Duo-ring. In this paper, as a generalization, we prove that the last characterization holds even if the ring is not a Duo-ring. Hence, we prove that a ring is a quasi-Frobenius ring if and only if it is an ring.

quasi-Frobenius ring, annihilator, injective, noetherian, artinian, cogenerator, annihilator, reflexive, finitely generated.