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In this paper, an improved design criterion for space-time trellis codes over time-correlated Rayleigh fading channels is presented. We decompose the time-correlated fading channel into two independent components: slow fading channel and fast fading channel. The code design problem for time-correlated fading channels is converted to the joint design both in slow fading channels and in fast fading channels, while no knowledge about correlation is needed. Simulation results are provided to confirm our theory.