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In this paper, we propose a new supervised linear feature extraction technique for multiclass classification problems that is specially suited to the nearest neighbor classifier (NN). The problem of finding the optimal linear projection matrix is defined as a classification problem and the Adaboost algorithm is used to compute it in an iterative way. This strategy allows the introduction of a multitask learning (MTL) criterion in the method and results in a solution that makes no assumptions about the data distribution and that is specially appropriated to solve the small sample size problem. The performance of the method is illustrated by an application to the face recognition problem. The experiments show that the representation obtained following the multitask approach improves the classic feature extraction algorithms when using the NN classifier, especially when we have a few examples from each class.