Frequent itemset generation is the prerequisite and most time-consuming process for association rule mining. Nowadays, most efficient Apriori-like algorithms rely heavily on the minimum support constraint to prune a vast amount of non-candidate itemsets. This pruning technique, however, becomes less useful for some real applications where the supports of interesting itemsets are extremely small, such as medical diagnosis, fraud detection, among the others. In this paper, we propose a new algorithm that maintains its performance even at relative low supports. Empirical evaluations show that our algorithm is, on the average, more than an order of magnitude faster than Apriori-like algorithms.