TCOM, an innovative data structure for mining association rules among infrequent items. Association rule mining is one of the most important areas in data mining, which has received a great deal of attention. The purpose of association rule mining is the discovery of association relationships or correlations among a set of items.In this paper, we present an efficient way to find the valid association rules among the infrequent items, which is seldom mentioned and whose importance often get ignored by other researchers. We design a new data structure, called Transactional Co-Occurrence Matrix, in short TCOM, by two passing of the original transactional database. Then the occurrence count of the itemsets and valid association rules will be mined based on TCOM, which combines the advantages of both transactional oriented (horizontal) layout and item oriented (vertical) layout of the database. It turns out that any itemsets could be randomly accessed and counted without full scan of either the original database or the TCOM, which significantly improves the efficiency of the mining processes.