The complementary M-ary orthogonal spreading with orthogonal frequency division multiplexing (CMOS-OFDM) is an efficient scheme for providing high bit error rate (BER) performance and low peak to mean envelop power ratio (PMEPR) in high frequency (HF) communications system. In the CMOS-OFDM, orthogonal spreading OFDM is implemented based on orthogonal complementary sequence pairs where there is an issue that one data symbol is transmitted through two OFDM symbols. In this paper, we present the M-ary orthogonal spreading OFDM scheme using complex complementary sequences which satisfy real domain orthogonality. The complementary real orthogonal spreading OFDM (CROS-OFDM) is restrict the PMEPR to 3dB and provides two times the bit rate of CMOS-OFDM. The CROS-OFDM scheme uses zero-center complementary sequences like the CMOS-OFDM and hence it is suitable to the HF OFDM and Wi-Fi system where the direct current subcarrier is not used. The simulation results show that the CROS-OFDM provides higher bit rate and BER performance.