Space-time (ST) trellis coded modulation (TCM) represents a high spectral efficiency technique for multiple antennas transmissions over fading channels. In literature, it was shown that ST-TCM technique offers full diversity when the rank criterion is met. However, “brute force” methods were used in almost all previous work to search for full diversity ST-TCM codes. In the present paper, we aim to derive an exact expression for the minimum coding gain distance (CGD) in the case of full diversity ST-TCM codes with minimum memory size, for two transmit antennas. Therefore, we transpose the ST-TCM design rules into operations over the set of modulo-M integer numbers (ZM), between the current trellis state and encoder’s input information symbol value, in order to derive the transmitted M-levels phase shift keying modulated (M-PSK) output values. In this context, a new design method is introduced to control the code’s minimum CGD value of full diversity ST-TCM schemes.