Let R be a ring with 1 and with a finite automorphism groap G and C the center of R and K = {g∈G|g(c)=c

c∈C}.Suppose R is Galois over R~G with Galois group G such that R~G is an Azumaya C~G-algebraThe main results of this paper are as follows:(1) If R~K is an Azumaya algebra over C

then R=A_cR~Kwheve A is Galois over C with Galois group K.Moreover

If the order of K is a unit in R

then R~K is Galois over R~K with Galois group G/K.(2) If R~K=CR~G and the order of K is a unit in R

then the results of (1) are true and R~K satisfies the Kanzaki hypothesis