Via a series of orthogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on U×U (U is the upper half-plane) with the measurey a 1 y a 1 dx 1 dx 2 dx 1 dx 2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness, Sp properties of them are established.