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In this paper, a channel precoding technique is proposed for M-ary continuous phase modulation (CPM) for multipath downlink channels. The proposed pre-equalizer, based on the approximation of CPM signals by complex exponential functions, applies modulo-arithmetic operations to ensure the stability as in Tomlinson-Harashima method. Spectrally efficient precoded signals are obtained with small envelope variations by employing a transmit antenna selection technique. Because the equalization functions are transferred to the base station, the complexity in the mobile terminals is reduced significantly. The simulation results depict the power spectral density of the transmitted signals and the bit-error rate. An upper bound on the error performance is computed and the relation between the number of transmit antennas and the spectral efficiency is derived.