Let $B$ be a Hirata separable and Galois extension of $B^G$ with Galois group $G$
of order $n$ invertible in $B$ for some integer $n$, $C$ the center of $B$, and
$V_B(B^G)$ the commutator subring of $B^G$ in $B$.
It is shown that there exist
subgroups $K$ and $N$ of $G$ such that $K$ is a normal subgroup of $N$ and one of the following three cases holds:
(i)
$V_B(B^K)$ is a central Galois algebra over $C$ with Galois group $K$,
(ii)
%the restriction of $N$ to $V_B(B^K)$ is isomorphic to $N$,
$V_B(B^K)$ is separable $C$-algebra with an automorphism group induced by and isomorphic with $K$, and
(iii)
$B^K$ is a central algebra over $V_B(B^K)$
and a Hirata separable Galois extension of $B^N$ with Galois group $N/K$.
More characterizations for a central Galois algebra $V_B(B^K)$ are given.