This paper discusses branch metric computation in the main decoder placed in an SST (Scarce State Transition) Viterbi decoder. The basic assumptions that all the message sequences are equally likely and that the channel is memoryless do not hold for the main decoder in an SST Viterbi decoder, when an inverse encoder or a pseudo-inverse encoder is used as a pre-decoder. Therefore, in contrast to a conventional method, an MAP (Maximum A Posteriori probability) estimation method itself, which is the starting point of the maximum likelihood decoding, has been applied to branch metric computation. Then, it has been clarified that the conventional branch metric computed in a usual SST Viterbi decoder happens to be equal to the branch metric derived using the MAP estimation method only for systematic codes. For general non-systematic codes, in particular, it has been found that it is impossible to decompose a path metric into such branch metrics that follow the original code trellis structure, because the branch metric derived at time k is also dependent on future state transitions.