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Selective mapping (SLM) is one of the most effective peak-to-average power ratio (PAPR) reduction techniques proposed for orthogonal frequency-division multiplexing systems. However, the fact that this technique requires the transmission of side information (SI), to enable the receiver to reverse the randomisation process before performing signal demodulation, can make it undesirable for certain applications as it degrades the system's bandwidth efficiency and, more significantly, the bit error rate (BER) performance. A modified SLM technique (MSLM) that can operate without the need for any dedicated SI for both channel-coded and uncoded scenarios while providing similar PAPR reduction performance as the ordinary SLM technique is proposed. It will be demonstrated that the proposed MSLM technique not only improves the system's bandwidth efficiency, but also achieves significantly better BER performance than the ordinary SLM technique.