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In this paper, we propose a new method for discovering hidden information from large-scale transaction databases by considering a property of cofactor implication. Cofactor implication is an extension or generalization of symmetric itemsets, which has been presented recently. Here we discuss the meaning of cofactor implication for the data mining applications, and show an efficient algorithm of extracting all non-trivial item pairs with cofactor implication by using Zero-suppressed Binary Decision Diagrams (ZBDDs). We show an experimental result to see how many itemsets can be extracted by using cofactor implication, compared with symmetric item set mining. Our result shows that the use of cofactor implication has a possibility of discovering a new aspect of structural information hidden in the databases.