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High peak-to-average power ratio (PAPR) of the transmitted signal is a major drawback of orthogonal frequency division multiplexing (OFDM). The selected mapping (SLM) technique is one of the promising PAPR reduction techniques for OFDM. In the SLM technique, some statistically independent data blocks are generated from an OFDM data block using a set of phase sequences and the one with the lowest PAPR is chosen and transmitted. In this paper, we propose an SLM technique with novel phase sequences. In the proposed SLM technique, it is not required to exchange side information between transmitter and receiver, which is usually required in the ordinary SLM technique. It is shown that we can achieve comparable PAPR reduction performance to the ordinary SLM technique with no data rate loss and a small increase in transmitted signal power.