Abstract: We have found a contour for integration of Faddeev equation which is different from the contour given by Cahill and Sloan. The essential point of our method is that a better mathematical expression of the kernel function for the Faddeev equation is given. With this expression, the values of the function in the neighbourhood of the origin can be calculated, whatever the values of l are. In the work of Cahill and Slcan only l=0, 1, 2, 3 can be rigorously calculated, but in this paper, we can calculate for l=0, 1, 2, ……, 8 rigorously.