Let $RG$ be a group ring of a group $G$ over a ring $R$ with 1,
$R_0$ the center of $R$,
$C$ the center of $RG$, and
$\overline G$ the inner automorphism group of the group ring $RG$ induced by the elements of $G$.
Characterizations are given for $RG$ which is a Hirata separable extension of $(RG)^{\overline G}$
and $C$ is a direct summand of $R_0G$ as a $C$-module.
Thus an Azumaya group ring $RG$ can be characterized in terms of Hirata separable extensions.
Moreover, it is shown that $RG$ is neither a Hirata separable extension
of $R$ nor a Galois extension of $(RG)^{\overline G}$ with Galois group $\overline G$.