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A simple control algorithm is proposed for a three-stage rearrangeable switching network with time division multiplexed links. The nonblocking condition is shown for the rearrangeable network controlled by the proposed algorithm. The rearrangeable nonblocking network controlled by the proposed method is more cost effective in hardware than a strictly nonblocking network for a large number of channels multiplexed on links. The computing complexity of the algorithms is not more than that for controlling the strictly nonblocking network. In the proposed algorithm, only one path must be moved in the rearrangement, thus reducing the difficulty in implementing the rearrangeable network. This algorithm is efficient for broadband switching systems or cross-connect devices where nonblocking switches are needed.