Fault equivalence is an essential concept in digital design with significance in fault diagnosis, diagnostic test generation, testability analysis and logic synthesis. In this paper, an efficient algorithm to check whether two faults are equivalent is presented. If they are not equivalent, the algorithm returns a test vector that distinguishes them. The proposed approach is complete since for every pair of faults it either proves equivalence or it returns a distinguishing vector. This is performed with a simple hardware construction and a sequence of simulation/ATPG-based steps. Experiments on benchmark circuits demonstrate the competitiveness of the proposed method.