In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation that involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expansion of the angular flux of neutrons leaking from the medium, in spherical harmonics with no assumption about the angular flux within the medium, gives a very good approximation of several classical plane geometry problems. These problems include the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, and the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method may be extended to other geometries.