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There have been a set of conversion matrices proposed recently by Wang and Ouyang to simplify the inverse fast Fourier transform (IFFT) computation involved in the selected mapping (SLM) scheme for reduction of the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. As compared to the conventional SLM scheme, the modified approach achieves close PAPR reduction with much lower complexity but degraded bit error rate (BER) performance. In this paper, we propose a new set of conversion matrices for the SLM scheme such that the complexity can be reduced without sacrificing the BER performance. It is shown that the improved SLM method has better BER performance and lower complexity than the previous work by Wang and Ouyang, at the cost of a slight PAPR reduction loss.