This paper presents a novel approach for implementation of the Viterbi algorithm, wherein survivor paths are generally kept in as low as one half of the storage required for traditional trace-back methods. Survivor memory reduction is obtained by storing only the useful part of the survivor paths. In other words, the redundancy in the survivor paths is removed. A decoder using this approach not only requires significantly less memory, but also runs faster than conventional decoders. Some instances of this approach are explicitly presented.