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The inhernet high peak-to-average power ratio (PAPR) of multicarrier transmission, such as OFDM or DMT, is a major drawback that can significantly worsen the power efficiency and performance of these systems. One of the most effective techniques proposed for reducing the PAPR in multi-carrier systems is based on selective mapping (SLM) in which a family of sequencies with random phase distribution is used iteratively to modify the phases of the modulated subcarriers with the aim to minimise the PAPR. However, the fact that this technique requires the transmission of side information, to enable correct demapping at the receiver, reduces the system's spectral and transmission-power efficiency. In this paper, we propose a modified SLM technique that does not require the transmission of any side information while at the same time it can achieve the same PAPR reduction and even lower symbol error rate (SER) performance as the unmodified SLM technique.