If the errors of a linear model are normally distributed and if quadratic loss is used, it is known, that the Gauss-Markov-estimatoris the best unbiased estimator of an estimable function η. Under certain conditions this is also true for convex loss. It we know only, that the error distribution lies in a certain class of distributions, and the normal distribution is in this class too, then, it is shown, thatbecomes minimax relative to this class.