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Max Frequent pattern mining is a essential technology and step in mining associations rules. Max frequent item sets contain the exact information of all the frequent itemsets. This paper proposed a fast algorithm for discovering maximuum frequent itemsets called FA-DMFI which can store attributes association information through scanning database only once. Then the max frequent itemsets is discovered in the association matrix by means of the bottom-up and top-down searching strategy. Therefore the algorithm execute time is reduced remarkably. mExperimental results show its effectiveness and efficiency.