Given A and B, how to find C if A = CBC?

Given

`A={{0,1,1,0},{1,0,0,-1},{-1,0,0,1},{0,1,1,0}} 

and

B={{0,1,0,0},{0,0,0,0},{0,0,0,1},{0,0,0,0}} 

and

A=C.B.C, how to find C?