Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric(RotS) function is special. For a RotS n variables function f(x_1,x_2,…,x_n) we have f(ρ~k_n(x_1,x_2,…x_n))=f(x_1,x_2,…,x_n) for k=0,1,…,n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary. Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric (RotS) function is special. For a RotS n variables function f (x_1, x_2, ..., x_n) we have f (ρ ~ k_n (x_1, x_2, ... In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, x, y, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.