Orthogonal frequency division multiplexing (OFDM) will continue to play an important role in the fifth generation (5G) of mobile communication enhanced mobile broadband (eMBB) scenario, however, the high peak-to-average power ratio (PAPR) of transmitted signals limits its further development. Selected mapping (SLM) is an effective method for PAPR reduction because it operates simply and introduces no distortion. Meanwhile, selecting the optimal phase sequence for SLM is vitally important, as the optimal phase sequence would bring better performance. This paper introduces Helmert sequence for PAPR reduction in SLM OFDM (SLM-OFDM) system (called Helmert-SLM), which is different from the other schemes using sequence such as random, Hadamard or Riemann. In addition, Helmert-SLM doesn't send any side information because the Helmert sequence has a regular structure. Analyses and simulation results also show that the Helmert-SLM scheme achieves extremely low PAPR. More specifically, it provides 3.5dB improvement compared to SLM-OFDM with Riemann sequence and 4.5dB improvement compared to SLM-OFDM with cyclic Hadamard sequence.