Aiming at how to produce infrequent itemsets in the negative association rules, this paper introduces vector inner product to this field. By converting the transaction database to the Boolean Vector Matrix, and by allotting a equitable data storage structure, we put forward a new algorithm to produce infrequent itemsets effectively. First of all, we convert a database to a Boolean Vector Matrix; and then calculate the inner vector in the matrix, and finally produce infrequent itemsets and frequent itemsets with the restriction of the 2LS model according to the idea of incremental change layer after layer ,which makes sure that infrequent itemsets not only can be produced by the joint of frequent itemsets , but also can be produced by the joint between infrequent itemsets and frequent itemsets, and between infrequent itemsets and infrequent itemsets .The experimental results show that this method not only scans the database only once, and also has the virtues such as dynamic pruning, without saving mid items, saving lots of memories, and without losing infrequent itemsets, which has an important meaning to the negative association rule mining and all kinds of itemsets with the characteristics of low frequent appearance, strong correlation in databases.