This paper presents an efficient and reliable method for the solution of multistage, multicomponent problems that involve the separation of highly non-ideal systems. The method uses a pseudo binary mixture (PBM) concept incorporated into the (Ishii, Y., & Otto, F. D. Cand. J. Chem. Eng., 51. (1973) 601-606) algorithm for stage-wise calculations. This algorithm solves the stage model equations simultaneously and structures the linearized equations such that matrix manipulations deal almost entirely with tridiagonal matrices. This greatly reduces computational time and computer storage requirements. Convergence characteristics for highly non-ideal systems are markedly improved by employing the PBM concept to account for the composition dependence of the equilibrium K-values. The advantages and simplicity of the original formulation of the Ishii and Otto (Ishii, Y., & Otto, F. D. Cand. J. Chem. Eng., 51. (1973) 601-606) algorithm are retained. The robustness of the method is illustrated with a number of difficult separation problems that are known to be highly sensitive to initial assumptions for temperature profiles.