Intrinsic image decomposition separates the input image into several layers which reflect the attributes of the scene. In this paper, we present a double-stream exchange transformer network for intrinsic image decomposition, in which an independent and interrelated relationship is built between reflectance and shading. There are two core designs in the double-stream exchange transformer network (DSETNet). First, we propose a novel exchange transformer block, which performs the information exchange and reconstruction between reflectance and shading components in a window-based self-attention. Second, a residual structure is added into the exchange transformer block to form a residual exchange transformer block to eliminate artifacts caused by local window areas. We predict reflectance and shading constraint relationship between reflectance and shading is established through residual exchange transformer block. The evaluation results on two real and synthetic public datasets BOLD and ShapeNet show that the DSETNet achieves competitive results with other advanced algorithms.