  In this paper, we introduce a class of rings which is a generalization of
reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and
$J(R)$ denote the Jacobson radical of $R$. A ring $R$ is called {\it
$J$-reflexive} if for any $a$, $b \in R$, $aRb = 0$ implies $bRa \subseteq
J(R)$. We give some characterizations of a $J$-reflexive ring. We prove that
some results of reflexive rings can be extended to $J$-reflexive rings for this
general setting. We conclude some relations between $J$-reflexive rings and
some related rings. We investigate some extensions of a ring which satisfies
the $J$-reflexive property and we show that the $J$-reflexive property is
Morita invariant.
