One of the main problems in pattern classification and neural network training theory is the generalization performance of learning. This paper extends the results on randomized linear zero empirical error (RLZEE) classifier obtained by Raudys, Dičiūnas and Basalykas for the case of centered multivariate spherical normal classes. We derive an exact formula for an expected probability of misclassification (PMC) of RLZEE classifier in a case of arbitrary (centered or non-centered) spherical normal classes. This formula depends on two parameters characterizing the “degree of non-centering” of data. We discuss theoretically and illustrate graphically and numerically the influence of these parameters on the PMC of RLZEE classifier. In particular, we show that in some cases non-centered data has smaller expected PMC than centered data.