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Association rule discovery is an important area of data mining. In dynamic databases, new transactions are appended as time advances. This may introduce new association rules and some existing association rules would become invalid. Thus, the maintenance of association rules for dynamic databases is an important problem. In this paper, promising frequent itemset algorithm, which is an incremental algorithm, is proposed to deal with this problem. The proposed algorithm uses maximum support count of 1-itemsets obtained from previous mining to estimate infrequent itemsets, called promising itemsets, of an original database that will capable of being frequent itemsets when new transactions are inserted into the original database. Thus, the algorithm can reduce a number of times to scan the original database. As a result, the algorithm has execution time faster than that of previous methods. This paper also conducts simulation experiments to show the performance of the proposed algorithm. The simulation results show that the proposed algorithm has a good performance.