Association rules mining is an important data mining problem that has been studied extensively. In this paper, a simple but Fast algorithm for Intersecting attributes lists using hash Tables (FIT) is presented. FIT is designed for efficiently computing all the frequent itemsets in large databases. It deploys an idea similar to Eclat but has a much better computational performance than Eclat due to two reasons: 1) FIT makes fewer total number of comparisons for each intersection operation between two attributes lists, and 2) FIT significantly reduces the total number of intersection operations. Our experimental results demonstrate that the performance of FIT is much better than that of Eclat and Apriori algorithms.