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Almost all the probabilistic decoding algorithms known for convolutional codes, perform decoding without prior knowledge of the error locations. Here, we introduce a novel maximum-likelihood decoding algorithm for a new class of convolutional codes named as the state transparent convolutional (STC) codes, which due to their properties error detection and error locating is possible prior to error correction. Hence, their decoding algorithm, termed here as the STC decoder, allows an error correcting algorithm to be applied only to the erroneous portions of the received sequence referred to here as the error spans (ESPs). We further prove that the proposed decoder, which locates the ESPs and applies the Viterbi algorithm (VA) only to these portions, always yields a decoded path in trellis identical to the one generated by the Viterbi decoder (VD). Due to the fact that the STC decoder applies the VA only to the ESPs, hence percentage of the single-stage (per codeword) trellis decoding performed by the STC decoder is considerably less than the VD, which is applied to the entire received sequence and this reduction is overwhelming for the fading channels, where the erroneous codewords are mostly clustered. Furthermore, through applying the VA only to the ESPs, the resulting algorithm can be viewed as a new formulation of the VD for the STC codes that analogous to the block decoding algorithms provides a predecoding error detection and error locating capabilities, while performing less single-stage trellis decoding.