Suppose that Tq, is a Toeplitz operator with a symbol 1> on the Hardy space H2 on the bidisc. Let N be a backward shift invariant subspace of H2, that is, N is an invariant subspace under r; and T:U. Let P be the orthogonal projection from H2 onto N. For 1> in H00 put Sq, = PTq,[N. In this paper, we give a characterization of a , backward shift invariant subspace which satisfies SzS S Sz
