The wavelet expansion is used in order to evaluate the angular dependence of the radiative intensity in the solution of the radiative transfer equation. The radiative intensity is expanded in terms of orthogonal Daubechies' wavelet basis in the angular domain. The method is applied to a two-dimensional rectangular enclosure with an absorbing, emitting and nonscattering medium in radiative equilibrium. One of the boundary surfaces is maintained at constant temperature T-1, while others are kept cold. This boundary conditions are chosen to demonstrate the effectiveness of the method in dealing with the geometries which are sensitive to ray effects. Centerline emissive power and surface heat flux distributions are compared well with the results given by the standard discrete ordinates method, the modified discrete ordinates method and also with the available exact solutions.