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We present an association rule mining method for mining high confidence rules, which describe interesting gene relationships from microarray datasets. Microarray datasets typically contain an order of magnitude more genes than experiments, rendering many data mining methods impractical as they are optimised for sparse datasets. A new family of row-enumeration rule mining algorithms have emerged to facilitate mining in dense datasets. These algorithms rely on pruning infrequent relationships to reduce the search space by using the support measure. This major shortcoming results in the pruning of many potentially interesting rules with low support but high confidence. We propose a new row-enumeration rule mining method, MaxConf, to mine high confidence rules from microarray data. MaxConf is a support-free algorithm which directly uses the confidence measure to effectively prune the search space. Experiments on three microarray datasets show that MaxConf outperforms support-based rule mining with respect to scalability and rule extraction. Furthermore, detailed biological analyses demonstrate the effectiveness of our approach -- the rules discovered by MaxConf are substantially more interesting and meaningful compared with support-based methods.