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In this paper, we first propose a novel multi-points square mapping (MSM) scheme. Then, we describe in detail how to combine the proposed MSM scheme with conventional partial transmit sequence (C-PTS) scheme, named as M-PTS, to reduce the PAPR of OFDM signals. Compared with C-PTS, the proposed M-PTS scheme needs not to submit side information while keeping almost the same performance of PAPR reduction as the C-PTS scheme. Extensive simulations are conducted to validate analytical results, showing that the proposed M-PTS scheme has better bandwidth efficiency and bit error ratio (BER) performance compared with the C-PTS scheme.