A joint design of modulation coding scheme for MIMO quasi-static fading systems is developed to provide high data rate and to minimize frame error probability. The main design idea is, at first, to decompose the MIMO system into multiple parallel SISO systems using singular value decomposition. Secondly, the design metric is obtained from an upperbound of pairwise error probability of the equivalent SISO systems. Thirdly, the joint design is obtained by finding the best asymmetric constellation and labeling of constellation points for a given baseline trellis structure of each SISO system through an exhaustive search. Simulation shows our joint design gives consistant performance gain.