Development of accurate and efficient methods for direct calculation of critical points is valuable for phase equilibrium calculations in chemical and petroleum engineering. A new method for critical points calculation is developed. For critical point calculation methods, the spinodal equation is given by setting to zero a determinant of nc (number of components) or nc-1 order, containing second-order derivatives of thermodynamic potentials. In this approach, this determinant has a lower order, which does not depend on the number of components in the mixture, but on the number of reduction parameters, with no restrictions on the binary interaction parameters (BIPs). The new method has been tested for several mixtures having various phase diagram shapes, and proved its reliability. The computation effort for each step for correcting temperature and molar volume can be significantly reduced. The proposed method is particularly efficient for mixtures with many components and few nonzero BIPs. Cubic two-parameter EOS are used; however, the proposed method can be applied for any EOS that observes the restrictions of the Reduction Theorem. (c) 2005 American Institute of Chemical Engineers.