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Association rule mining has many achievements in the area of knowledge discovery. However, the quality of the extracted association rules has not drawn adequate attention from researchers in data mining community. One big concern with the quality of association rule mining is the size of the extracted rule set. As a matter of fact, 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 reliable exact association rule basis from which more concise nonredundant rules can be extracted. We prove that the redundancy eliminated using the proposed reliable association rule basis does not reduce the belief to the extracted rules. Moreover, this paper proposes a level wise approach for efficiently extracting closed itemsets and minimal generators — a key issue in closure based association rule mining.