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Efficient algorithms for mining frequent itemsets are crucial for mining association rules. Most existing work focuses on mining all frequent itemsets. However, since any subset of a frequent set also is frequent, it is sufficient to mine the set of frequent closed itemsets which determines exactly the complete set of all frequent itemsets and is usually much smaller than the laster. In this paper, we study the performance of the existing approaches for mining frequent closed itemsets. We also develop an algorithm, called FCFIA. In this algorithm, we develop and integrate two techniques in order to improve the efficiency of mining frequent closed itemsets. We also present experimental results which show that our method outperforms the existing methods FPclose.