On a factorization of homeomorphisms of the circle possessing periodic points

We prove that for every orientation-preserving homeomorphism F : S1→S1 possessing periodic points of order n there exist a homeomorphism T : S1 →S1 such that T n = id and a homeomorphism G: S1 →S1 without periodic points except fixed points such that F = T q ◦G for an integer 1 q