We show that if the stable rank of $B^{alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{alpha}$-module B.