To remedy discontinuous boundary conditions, we propose the spatial and angular domain decomposition approach for the solution of radiative transfer equation (RTE) in a two-dimensional rectangular enclosure. The RTE is angularly and spatially discretized. For each spatial node, the total solid angle 4π is decomposed into several angular sub-domains according to the distribution of discontinuous boundaries, and the quadrature weighting factors are recalculated for each angular sub-domain by using the compound trapezoidal integral scheme. For each angularly-discretized direction, the spatial domain is decomposed into a few spatial sub-domains according to the distribution of discontinuous boundaries. In each spatial sub-domain the distribution of radiative intensity is continuous, and the angularly-discretized RTE is solved for each spatial sub-domain. Two examples are employed to verify the performance of the domain decomposition method, and the results confirm its suitability and advantage for treating radiative transfer problem with discontinuous boundary conditions.