Abstract: In the present paper, a new plate-to-plate method is developed for performance prediction of ideal systems and those close to ideal ones. The sum ofmole fractions of heavy components in the top product, ∑HP, as well as mole fraction ratios of heavy components in the upper part of a column and those of light components in the lower part, vij s and μij s, are selected as iterative variables instead of individual concentrations. Two parallel iterations are suggested. The first one is for ∑HP. The mole fractions of various light components are calculated top-down towards the match plate. The mole fraction of various heavy components are calculated bottom-up towards the match plate. ∑HP is then relaxed with the total match tolerance of heavy components. The second one is for vijs and μijs. The subsequent guess of vijs and μijs is calculated from the solution of tridiagnol matrices with the phase equilibrium constants Kijs obtained from the plate-to-plate calculation. Consequently, the related loops consist of a single strong loop accompanied by a number of comparatively insignificant loops. Thus, a multi-variable system can be converted into a single variable system and the convergence can be dramatically accelear-ated. A rapid and stable convergence is finally achieved. This procedure has been successfully used for complex columns with multifeed and multi-side-stream .