This paper describes a simple method of adapting the relativistic Hartree-Fock approximation to configurations involving open shells. A shell with angular quantum number / splits relativistically into subshells with j - l + 1/2 and j = l - 1/2, and the electrons can distribute themselves between these subshells in several different ways, giving rise to several different configurations, having very nearly equal energies. The idea of an average of configurations is extended to give a weighted average of all the terms arising from all these configurations. The Hartrer Fock wave functions are then determined for this average configuration ; the full Hamiltonian matrix can then be determined, and the energy level scheme found. Results are given for the (2 p)3 ground configuration of Nitrogen