Item set mining has been an active area of research due to its successful application in various data mining scenarios including finding association rules. Though most of the past paper has been on finding frequent item sets, infrequent item set mining has demonstrated its utility in web mining, bioinformatics and other fields. In this paper, the authors propose a new method based on Apriori algorithm to find infrequent item sets and non-present item sets. Finally, they analyze the behavior of their proposed method by considering a transactional data base.