A scale-shift approach is introduced to further refine the pseudo-binary-mixture (PBM) simultaneous correction procedure for the solution of multicomponent, multistage separation problems [Ishii, Y., & Otto, F. D. (2001). An efficient simultaneous correction procedure for multicomponent, multistage separation calculations for non-ideal systems. Computers and Chemical Engineering, 25, 1285-1298; & Ishii, Y., & Otto, F. D. (2003a). A method to extend the domain of convergence for difficult multicomponent, multistage separation problems. Computers and Chemical Engineering, 27, 855-868]. The scale-shift approach takes advantage of the fact that a solution to a stage-wise separation problem is more easily obtained the fewer the number of stages. In the approach the column specified in a given problem is initially downsized to a configuration having a small number of stages and then scaled up to the original one in a multiple-step manner. A solution is obtained at each scale-shift step and the results are used as a set of initial assumptions to solve the subsequent scaled-up problem. Combining the scale-shift approach along with the gradual non-ideal enhancing method with the PBM algorithm provides a more robust and efficient algorithm for the simulation and solution of difficult multicomponent, multistage separation problems including those involving non-ideal mixtures that are highly sensitive to the quality of initial values. A geometric consideration for the gradual non-ideal enhancing method and details of the unique procedure for the algebraic inversion of matrices employed in the algorithm are also presented. (C) 2004 Elsevier Ltd. All rights reserved.