In this paper we give a new proof to Theorem 1 in Gu and Zheng (1997) . We then provide that T f T g = 0 if and only if f (z, w) or g(z, w) is identically zero where T f and T g are two level Toeplitz operators with generating functions f (z, w) and g(z, w) being two variables bounded measurable functions on the unit circle . We also conjectured zero product of three two level Toeplitz operators.