Association rule mining has made many achievements in the area of knowledge discovery in databases. Recent years, the quality of the extracted association rules has drawn more and more attention from researchers in data mining community. One big concern is with the size of the extracted rule set. Very often tens of thousands of association rules are extracted among which many are redundant thus useless. In this paper, we first analyze the redundancy problem in association rules and then propose a novel ATMS-based method for extracting non-redundant association rules.