  In studying commutants of analytic Toeplitz operators, Thomson proved a
remarkable theorem which states that under a mild condition, the commutant of
an analytic Toeplitz operator is equal to that of Toeplitz operator defined by
a finite Blaschke product. Cowen gave an significant improvement of Thosom's
result. In this paper, we will present examples in Cowen's class which does not
lie in Thomson's class.
