In 3G wireless data networks, network operators would like to balance system throughput while serving users fairly. This is achieved through the use of fair scheduling. However, this approach provides non-Pareto optimal bandwidth allocation when considering a network as a whole. In this paper an optimal offline algorithm that is based on the decomposition result for a double stochastic matrix by Birkhoff and von Neumann is proposed. A utility max-min fairness is suggested for the derivation of a double stochastic matrix. Using a numerical experiment, new approach improves the fairness objective and is close to the optimal solution.