This letter presents a new concatenated code and a new criterion for the new concatenated code in fast Rayleigh fading channel. The new concatenated code consists of the cascade of a new space-time trellis code (STTC) as an inner code and a new convolutional code as an outer code. The new criterion maximizes the minimum free distance for the new convolutional code and both the minimum trace and the average trace of distance matrix for the new STTC. The new concatenated code improves the frame error rate (FER) performance significantly with low complexity. The new STTC and convolutional code are designed so as to satisfy the new criterion for 4-state 4 phase shift keying (PSK). The results of the suggested concatenated code are obtained using two transmit antennas, and shown to be significantly superior to the new and existing STTCs. As the number of receive antennas increases, the performance of the new concatenated code significantly improves, for instance, reaches FER = 10-3 at signal-to-noise ratio (SNR) = 5.2 dB for four receive antennas. Note that the proposed concatenated code also improves significant FER performance by using only one receive antenna for high SNR.