In this paper, we present an efficient method for the prediction of homogeneous azeotropes. The method is an adaptation of a former method based on interval analysis techniques. An interval Newton with generalized bisection (IN/GB) technique is used to find all the roots of a set of equations representing the azeotropy condition. The novel contribution is to combine this robust technique with the Zharov-Serafimov topological index theory. By checking the topological consistency, it is possible to avoid the numerical verification of the nonexistence and therefore to reduce significantly the total computation time. In addition, a simplified model is selectively used at the first stage of the algorithm for providing good starting points for the second stage, where the full model is used for solution refining. In this way, more computation time is saved without compromising the reliability of the method. As a result, the performance of the method is comparable to the one of the fastest local methods.