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In this paper, we propose a novel algorithm for rule extraction from support vector machines (SVMs), termed SQRex-SVM. The proposed method extracts rules directly from the support vectors (SVs) of a trained SVM using a modified sequential covering algorithm. Rules are generated based on an ordered search of the most discriminative features, as measured by interclass separation. Rule performance is then evaluated using measured rates of true and false positives and the area under the receiver operating characteristic (ROC) curve (AUC). Results are presented on a number of commonly used data sets that show the rules produced by SQRex-SVM exhibit both improved generalization performance and smaller more comprehensible rule sets compared to both other SVM rule extraction techniques and direct rule learning techniques.