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Bayesian network (BN) is applied to the field of fault diagnosis to improve the inference ability of fault diagnosis. Therefore, fault Bayesian network (FBN) for the complex systems is proposed, and the inference method using FBN to make fault diagnosis is given in the paper. In the given method, inference of fault diagnosis includes the following processes: mapping complex systems into fault Bayesian network, transforming inference structures, initializing beliefs, propagating and absorbing beliefs and computing probability distributions. Besides, corresponding computing methods are given. At last, the proposed method is exemplified by a fault diagnosis of a digital circuit system.