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One of the main issues of orthogonal frequency division multiplexing (OFDM) is the high peak-to-average power ratio (PAPR) of the transmitted signal which adversely affects the complexity of power amplifiers. The selected mapping (SLM) technique is one of the promising PAPR reduction techniques for OFDM. In this reported work, rows of normalised Riemann matrices are selected as phase sequence vectors for the SLM technique. MATLAB simulations show PAPR reduction of around 2.3 dB using the proposed method compared with methods reported in the literature.