Point matching via corresponding circles (ICC) is a technique for removing outliers (mismatches) from given putative point correspondences in image pairs. It can be used as a basis for a wide range of applications including structure-from-motion, 3D reconstruction, tracking, image retrieval, registration, and object recognition. In this paper, we propose a new method called Fast Identification of point correspondences by Corresponding Circles (FICC) that improves the quality of the rejection mismatches and reduces the cost of computing it. In particular, we propose a new strategy that aims to take better advantage of the corresponding circles and reduces the number of putative points correspondences tested by the corresponding circles in each iteration rather than all set of putative correspondences, as in the original ICC. This reduces the computing time and together with a more efficient tool for rejecting mismatches which leads to significant gains in efficiency. We provide comparative results illustrating the improvements obtained by FICC over ICC, and we compare with many state-of-the-art methods.