The techniques for fitting boundary conditions in the cellular method are discussed. A difficulty that has often arisen in this respect is illustrated and its origin explained. A new method is introduced that involves the development of a technique for dealing with a least squares problem for a system of homogeneous equations subject to a subsidiary condition. A program for a digital computer is described which carries out the cellular computation in an entirely automatic fashion. As a part of this program, a simplified method to integrate Schrodinger's radical equation in floating-point form is described. The energy eigenvalues for all the 12 irreducible representations for k = 0 for zirconium metal are given.