Summary: Effective knowledge integration plays a very important role in knowledge engineering and knowledge-based machine learning. The combination of Bayesian networks (BNs) has shown a promising technique in knowledge fusion and the way of combining BNs remains a challenging research topic. An effective method of BNs combination should not impose any particular constraints on the underlying BNs such that the method is applicable to a variety of knowledge engineering scenarios. In general, a sound method of BNs combination should satisfy three fundamental criteria, that is, avoiding cycles, preserving the conditional independencies of BN structures, and preserving the characteristics of individual BN parameters, respectively. However, none of the existing BNs combination method satisfies all the aforementioned criteria. Accordingly, there are only marginal theoretical contributions and limited practical values of previous research on BNs combination. In this paper, following the approach adopted by existing BNs combination methods, we assume that there is an ancestral ordering shared by individual BNs that helps avoid cycles. We first design and develop a novel BNs combination method that focuses on the following two aspects: (1) a generic method for combining BNs that does not impose any particular constraints on the underlying BNs, and (2) an effective approach ensuring that the last two criteria of BNs combination are satisfied. Further through a formal analysis, we compare the properties of the proposed method and that of three classical BNs combination methods, and hence to demonstrate the distinctive advantages of the proposed BNs combination method. Finally, we apply the proposed method in recommender systems for estimating users’ ratings based on their implicit preferences, bank direct marketing for predicting clients’ willingness of deposit subscription, and disease diagnosis for assessing patients’ breast cancer risk.