In this paper, we propose a new ordered statistics decoding (OSD) for linear block codes, which is referred to as local constraint-based OSD (LC-OSD). Distinguished from the conventional OSD, which chooses the most reliable basis (MRB) for re-encoding, the LC-OSD chooses an extended MRB on which local constraints are naturally imposed. A list of candidate codewords is then generated by performing a serial list Viterbi algorithm (SLVA) over the trellis specified with the local constraints. To terminate early the SLVA for complexity reduction, we present a simple criterion which monitors the ratio of the bound on the likelihood of the unexplored candidate codewords to the sum of the hard-decision vector’s likelihood and the up-to-date optimal candidate’s likelihood. Simulation results show that the LC-OSD can have a much less number of test patterns than that of the conventional OSD but cause negligible performance loss. Comparisons with other complexity-reduced OSDs are also conducted, showing the advantages of the LC-OSD in terms of complexity.