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This paper discusses classification using support vector machines in a normalized feature space. We consider both normalization in input space and in feature space. Exploiting the fact that in this setting all points lie on the surface of a unit hypersphere we replace the optimal separating hyperplane by one that is symmetric in its angles, leading to an improved estimator. Evaluation of these considerations is done in numerical experiments on two real-world datasets. The stability to noise of this offset correction is subsequently investigated as well as its optimality.