In this work, a modification to the well known and extensively used Tridiagonal Matrix Method, proposed, since 1966 by Wang and Henke (1966), for simulating problems is proposed for promoting the convergence of the original iterative process. The modification, which involves the incorporation of Broyden's method for accelerating convergence based on adjustment of the tear variables, solves the vapour-liquid multi-stage distillation problems in a more efficient way. Two promotion schemes are proposed, one uses as the tear variables the temperature and vapour flow profiles and the other uses only the temperature profile. The two promotion schemes are compared to the original iteration scheme proposed by Wang and Henke. Results are reported for distillation and reboiled-absorption processes.