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) V_B(B^K) is separable C-algebra with an automorphism group induced by and isomorphic with K, and (iii) BK 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 VB(B^K) are given.