We present a new method for the approximate solution of the Bethe-Goldstone equation when it has a singular kernel. The method reduces the integral equation to a set of coupled differential equations which are easily solved. In the special case of binding energy calculations, non-singular kernel, our method is equivalent to the reference spectrum method. A particular advantage is that there is no ambiguity in the treatment of hard-core N-N interactions. We perform calculations both for the Hamada-Johnston and Reid hard-core internucleon potentials and in intermediate states always use self-consistent single-particle energies. We apply the method to calculate in nuclear matter the binding energy/nucleon and the nucleon optical potential. Our results for the binding energy differ by about 2 MeV from those published for similar calculations. The difference is a consequence of our use of self-consistent energies and a greater number of partial waves, L ≦ 4. For the optical potential we obtain a logarithmic variation with incident energy E for E > 100 MeV, in agreement with experimental data. We also obtain better agreement with experiment than other authors for the energy variation in the the range 40 MeV < E < 100 MeV. This improvement is a consequence of our use of a higher number of partial waves.