Viterbi algorithm is the basic technique for space-time trellis codes (STTC) decoding. The received information affected by the channel impairments can be corrected by the path record determined by accumulating the branch metrics in the state transitions. However, the computation complexity of the branch metric accumulation in STTC Vitebri decoding is extremely high in spite of the well error-correction capacity. Moreover, the computational complexity also increases significantly if the number of antennas and the order of modulation increase. To reduce the computational burden, we propose a new method to compute the branch metrics in the geometric view. The degree of complexity reduction is very impressive at sacrifice of a little degradation of coding gain. Furthermore, more complexity reduction can be achieved when more antennas and higher order of modulation are applied.