This work describes an algorithm that uses the Heidemann and Khalil (1980, A.I.Ch.E. J., 26, 769-779) critical point criteria and a homotopy continuation technique for calculating critical loci in binary mixtures. This approach is able to track smoothly transition from G/L critical points to L/L critical points without the need of changing initial estimates. Such transitions marked by the existence of a turning point in the critical locus are commonly found in type III and IV mixtures. The tangent plane global stability tests are included to locate UCEPs and LCEPs which are intersections of the critical locus and the LLG line. The continuation method is as efficient as a gradient-based approach like Heidemann and Khalil's method and as robust as the Hicks and Young's grid-search approach. It also provides physical insight to the change in phase behavior as the composition and the equation of states parameters change.