It is shown that the semi-discrete ordinates equation can be used to create a computer program for a general order of PL approximations for solving the multigroup neutron transport equation in two-dimensional x-y geometry. Sample calculations for problems using up to a P7 approximation and up to four energy groups are given, and the results are compared with corresponding ones obtained by the discrete ordinates method. As the order of approximations increases, both results show good agreement, when the influence of the ray effect is not appreciable. The advantage of the present method is that the ray effect does not occur, which is the problem in the discrete ordinates method.