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A machine learning algorithm using evolutionary algorithms and Support Vector Machines is presented. The kernel function of support vector machines are evolved using recently introduced Gene Expression Programming algorithms. This technique trains a support vector machine with the kernel function most suitable for the training data set rather than pre-specifying the kernel function. The fitness of the kernel is measured by calculating cross validation accuracy. SVM trained with the fittest kernels is then used to classify previously unseen data. The algorithm is elucidated using preliminary case studies for classification of cancer data and bank transaction data set. It is shown that the Evolutionary Support Vector Machine has good generalization properties when compared with Support Vector Machines using standard (polynomial and radial basis) kernel functions.