Phase stability testing is an important sub-problem in phase equilibrium calculations, which require the most important computational effort in reservoir compositional simulations and some process simulators. In this work, a new reduction method for phase stability analysis is proposed. Based on the multi-linear expression of the logarithm of fugacity coefficients as functions of some component properties (elements of the reduction matrix) and of the coefficients depending only on the reduction parameters, a new set of independent variables (which are unbounded, unlike reduction parameters) and the related set of error equations are proposed. Second order Newton iterations are directly used, without the need of switching from successive substitution iterations. It is shown that the proposed method has the same convergence path as the conventional method (in the compositional space) using the logarithm of formal mole numbers as independent variables. Besides, the proposed primary variables are Lagrange multipliers corresponding to a constrained minimization of the modified tangent plane distance function with respect to a specific set of variables and constraints. The robustness and the efficiency of the proposed method are tested for several synthetic and reservoir mixtures, and it compares favorably to conventional and previous reduction methods. Several interesting features are discussed, and a link between conventional and reduction methods is presented. (C) 2013 Elsevier B.V. All rights reserved.