Letbe a stochastic matrix defining an irreducible, aperiodic, reversible and positive-recurrent Markov chain. Letbe a partition of the circle into setsSiach consisting of finite union ofarcsAkl. Letftbe a rotation of length t of the circle and denote Lebesgue measure by λ. We generalize and prove for the matrix P a theorem (conjecture) of Joel E. Cohen (n=2), and S. Alpern and S.Kalpazidou (n≥2) asserting that any nxn recurrent stochastic matrix (rij) is given byfor some choice of rotation ft and partition {Si}