In solving the two-group, two medium equations for neutron diffusion in a finite one-dimensional multiplying system, the equations in each medium can be solved, and the boundary conditions used to determine the coefficients. This direct attack involves eight simultaneous linear equations. The opportunities for error are numerous, and, frequently, a great deal of accuracy is lost by subtractions; hence, it is felt that an alternative method of solution, in which numerical errors would be less likely to occur, would be desirable.