We use end-to-end measurements to address the problem of fault diagnosis in computer networks. Since link-level characteristics cannot be uniquely determined from available end-to-end measurements, most existing diagnosis approaches make statistical assumptions of the network to obtain a unique solution. However, the performance of these approaches is not assured due to the uncertainty of the assumptions. Thus the diagnostic accuracy cannot be guaranteed. In this paper, we propose a different paradigm for fault diagnosis which can find all identifiable links and the minimal identifiable link sequences, and infer their loss rates with the least error. Compared with a former representative diagnosis method through experiments, the experimental results show that our method has smaller diagnosis granularity and much less running time for most network topologies. We also conducted experiments using 105 Planetlab hosts. The results validate the performance of our method as well.