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Unitary space-time (UST) symbol-based turbo code has recently been proposed which can reduce the system complexity and calculation amount compared with bit-wise concatenation scheme. However, the corresponding maximum a posteriori (MAP) decoding algorithm still makes hardware unbearable and later its simplified versions, max-log-MAP and log-MAP algorithms, appeared. In this paper, we propose a multi-ary soft output Viterbi Algorithm (SOVA) decoding algorithm for UST symbol-based turbo code. Using our UST symbol-based SOVA, soft output information from the prior iteration can be accepted as the a priori information for current iteration. Notably, the experimental results show that our algorithm can achieve close performance to max-log-MAP and log-MAP algorithms with lower complexity. The performance of the SOVA and that of MAP algorithm are almost the same at a BER of 10-5, and is even better for a higher BER.