The mathematical analysis of many astrophysical problems involving radiative transfer is so complicated that it is necessary to have recourse to numerical approximations to the radiative transfer equation. This paper describes an extension, for use in radiation problems, of Carlson's S n difference approximation, which has been extensively used in neutron transport problems owing to its simplicity, its suitability for electronic computation, and its accuracy. Illustrations are provided to show the application of the new method in spherical problems with both scattering and non-scattering source terms, and the method has also been used to give an approximate solution to the Milne problem for a plane-parallel isotropic scattering grey atmosphere having constant net flux.