In recent years space-time trellis codes (STTCs) have attracted a great amount of research interest in wireless communication. However, the design criterion for STTCs is still a difficult problem. In flat fast fading channels, when the number of antennas is large, the space-time trellis codes design criterion, which is based on maximizing the minimum squared Euclidean distance, is better than the traditional distance and product criteria. Nevertheless, the former criterion is still not perfect. In this paper, from the aspects of squared distance distribution and squared distance sum-square square-sum ratio distribution, an improved criterion is presented, and some new codes are also obtained, which are the best codes known. In addition, a new reason is given, which can explain the different performance of a code between in slow fading channels and in fast fading channels. Finally the improved criterion is introduced into the design of smart-greedy codes.