It is shown that the discrete ordinate method of Chandrasekhar (1960) as applied to the photoelectron transport problem by Stolarski (1972) allows the expression of the backscattered angular intensity in terms of Chandrasehkar's H function. From this expression several exact relations have been obtained. The emergent intensity has in particular been exactly determined both for the case of an isotropic incident beam with no internal source and for the case of no incident beam and a constant internal source. The escape flux is also easily estimated. The accuracy to be expected in lower orders of approximation depends crucially on a proper choice of quadrature formula and is indicated by comparing the H function for the two-stream approximation to its 'exact' value. These new results provide useful additional insight into some important aspects of the transport problem. For example, it is explicitly revealed how the angular distribution of the backscattered intensity depends on the assumed variation of the internal source with depth and on the assumed angular variation of the incident beam.