The global phase diagram of a system of charged hard spheres, composed of positive and negative ions of the same size, is obtained by means of computer simulations. Thermodynamic integration and Einstein crystal calculations are used to determine the free energies of the different possible solid structures. In this way, the fluid-solid and solid-solid phase transitions are located. Gibbs-Duhem integration is used to trace the full coexistence curves between the different phases involved. Three different solid structures are found to be stable for the model considered; namely, a cesium chloride structure (CsCl), a substitutionally disordered close packed structure which is faced centered cubic (fcc), and a tetragonal ordered structure with a fcc arrangement of atoms if the charge of the ions is not considered. At high temperatures, freezing leads to the substitutionally disordered close packed structure. This solid structure undergoes an order-disorder transition at low temperatures transforming into the tetragonal solid. At low temperatures freezing leads to the cesium chloride structure (CsCl) which undergoes a phase transition to the tetragonal structure at high pressures. The tetragonal solid is the stable solid phase at low temperatures and high densities. In a narrow range of temperatures direct coexistence between the fluid and the tetragonal solid is observed. Three triple points are found for the model considered. The usual vapor-liquid-CsCl solid triple point occurs at T-*=0.0225. In addition, a fluid-fcc disordered-tetragonal triple point is located at T-*=0.245 and, finally, a fluid-CsCl-tetragonal triple point appears at T-*=0.234. The results presented here can be used to test the performance of the different theoretical treatments of freezing available in the literature. (C) 2003 American Institute of Physics.