In this work, we study briefly on the multiple trellis coded modulation (MTCM) which is found in literature as a way of increasing the performance of the system. An MTCM system provides better performance than a TCM counterpart without increasing the bandwidth and complexity of the system. This is illustrated by giving the rate 1/2 trellis coded modulation (TCM) and the rate 2/4 MTCM schemes as examples. Equations of upper bounds on their bit error probabilities are evaluated by assuming that they are transmitted over an AWGN and a slowly fading Rician communication channels. A comparison is made by plotting upper bounds of bit error probabilities as functions of Eb/N0. by using these equations. The comparison yields that the upper bound on the bit error probability of the rate 2/4 MTCM scheme is lower than that of the rate 1/2 TCM scheme for both cases.