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A new iris feature extraction approach using both spatial and frequency domain is presented. Steerable pyramid is adopted to get the orientation information on iris images. The feature sequence is extracted on each sub-image and used to train Support Vector Machine (SVM) as iris classifiers. SVM has drawn great interest recently as one of the best classifiers in machine learning, although there is a problem in the use of traditional SVM for iris recognition. It cannot treat False Accept and False Reject differently with different security requirements. Therefore, a new kind of SVM called Non-symmetrical SVM is presented to classify the iris features. Experimental data shows that Non-symmetrical SVM can satisfy various security requirements in iris recognition applications. Feature sequence combined with spatial and frequency domain represents the variation details of the iris patterns properly. The results in this study demonstrate the potential of our new approach, and show that it performs more satisfactorily when compared to former algorithms.