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This paper presents the application of a genetic algorithm (GA) and a support vector machine (SVM) to the recognition of blood cells based on the image of the bone marrow aspirate. The main task of the GA is the selection of the features used by the SVM in the final recognition and classification of cells. The automatic recognition system has been developed, and the results of its numerical verification are presented and discussed. They show that the application of the GA is a powerful tool for the selection of the diagnostic features, leading to a significant improvement of the accuracy of the whole system.