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Privacy concerns often prevent different parties from sharing their data in order to carry out data mining applications on their joint data. Privacy-preserving data mining provides a solution by creating distributed data mining algorithm in which the underlying data is not revealed. In this paper, we address a particular data mining problem, learning the structure of Bayesian network on distributed heterogeneous data. In this setting, three or more parties owning confidential databases wish to learn the structure on the combination of their databases without revealing anything about their data to each other. We provide a private generalized scalar product share protocol for learning the empirical entropy. Then we give an effective and privacy-preserving version of the B&BMDL algorithm to construct the structure of a Bayesian network for the parties' joint data. In comparison to the previously known solution for this problem (Wright and Yang, 2004), which is based on K2 algorithm, our solution provides complete accuracy, full privacy, ideal universality, and better performance. In particular, our solution provides fully private, in that the only thing the parties learn about each other's inputs is the desired output and the number of stochastic variables' value, and more universal, in that the databases partitioned vertically are among three or more parties, and completely accurate, in that the structure computed are exactly what they would be if the data was centralized. In addition, our solution works for both binary and non-binary discrete data.