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Support Vector Machines (SVMs) are originally designed for the solution of two-class problems. In multiclass applications, several strategies divide the original problem into binary subtasks, whose results are combined. In a previous work, Genetic Algorithms were used to determine the combination of binary SVMs in a multiclass solution. In order to improve the classification performance obtained, this algorithm was extended to search the parameter values of the binary SVMs contained in the decompositions. This paper presents results of the proposed algorithm in four datasets, with encouraging results.