IRIS biometric is one of the most efficient and trusted biometric methods for authenticating users owing to invariance with age or with physical activities. IRIS recognition techniques are broadly categorised in three groups: phase, texture and kernel-based methods, which out of kernel-based methods are proven to be the best suited for IRIS recognition problem. In this work a multiclass kernel Fisher analysis and its consequent feature set for IRIS recognition is proposed. The authors use support vector machine (SVM) classifier to group the large database into smaller groups where each group is linearly separable from the other. Once an image is grouped as one of the groups by SVM, it is classified to be recognised by hidden Markov model (HMM) classifier which compares the features of the given image only with the other images of the same group. Results show 93.2% overall accuracy for the system if we consider seven features and improved to 99.6% when 1200 features are used. In order to meet this efficiency an average convergence time needed by the algorithm is found to be lesser than existing SVM-based technique. Results also show fast convergence time for optimisation process in comparison to with other conventional kernel and SVM-based techniques.