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Finding the matrix with the maximum singular value amongst a set of matrices is a common problem occurring in transmit signal processing algorithms for multiuser multiple-input multiple-output (MIMO) systems. However, computing the principal singular value of a matrix is a rather numerically complex task. Furthermore, in many practical scenarios, the number of users is large and for each user this task has to be conducted. In this paper we therefore propose a novel user preselection method which reduces the computational complexity at no performance loss. This is achieved by deselecting some users based on a simple criterion and thus avoiding explicit computations of the singular values of those users. This criterion is based on easily computable bounds for the principal singular values. Finally, a statistical analysis is provided and the application to the Successive Encoding Successive Allocation Method (SESAM) is shown.