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In this paper, an efficient method to improve the performance of the box and matching algorithm (BMA) is presented. By constructing a control band which is error free with high probability, we enhance the matching capability of the BMA. More precisely, the performance of BMA of order (i+1) is nearly achieved with a linear increase in complexity and no increase in memory with respect to BMA of order i. Simulation results show that the performance of the enhanced BMA with a finite number of random biasing iterations for the decoding of the RS(255,239) code is about 0.1 dB away from that of maximum likelihood decoding (MLD) at the word error rate (WER) 10-3. A tight performance analysis is derived based on the theory of order statistics for this new approach.