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The development of multimedia services in cellular radio systems requires effective control on the transmission rates of users. In this paper, a novel joint power and rate control algorithm is proposed for multi-rate cellular radio systems. It attains the maximum throughput with minimum transmission powers. Simulations results show that the power consumption performance of the proposed algorithm is better than selective power control (SPC) algorithm in feasible systems. In infeasible systems, both of its throughput and power consumption performance exceed those of SPC.