The non-linear distortion caused by high peak-to-average power ratio (PAPR) of transmitted signal is a major drawback in the OFDM systems. In this paper, the proposed PAPR reduction scheme is to choose the corresponding symbol patterns with a low PAPR in the expanded signal space. However, the scheme has a high complexity for the selection of symbol pattern with the smallest signal power in a larger expanded signal space. The scheme could be realized as a signal mapping from the original information symbols to the corresponding patterns. With the selection of the corresponded symbol patterns, the PAPR could be greatly reduced. According to the simulation results with the proposed scheme, while the length of the data frame is 16 and the signal expansion with adding 1 bit and 2 bits, the PAPR changing rate could be 20 percents and 16 percents of the original PAPA, respectively. However, there is no prominent improvement on PAPR reduction with more than 8 bits for using the signal expansion scheme.