This Note reports remarkable improvements in the previously reported mathematical model for multi-component separating cascades, which are applicable to the cases where the interstage flows and the stage separation factors are input variables for the calculations. The number of the independent variables is greatly decreased for much more efficient iterative calculations by the multidimensional Newton-Raphson method. Particularly, if the stage separation factors are independent of concentrations of the up and down streams, the improved model presents great decreases both in the computation time needed at each iterative step and in the number of total iterations. Several numerical experiments made for a five-component system of N2-O2-41 Ar-85Kr-133Xe, which are separated by using the porous membrane method, indicate that the total computation time is shortened by almost two orders of magnitude if the improved model is used.