The Orthogonal Frequency Division Multiplexing (OFDM) has emerged as one of the promising techniques because of its robustness to multipath fading with high-speed data transmission. Classical bipolar OFDM cannot be used in intensity modulated with direct detection (IM/DD) optical communication systems, as visible light communication (VLC), so many optical modulation techniques as asymmetrical clipped optical OFDM (ACO-OFDM) and DC-Clipped OFDM (DCO-OFDM) have been investigated. In this paper, we introduce a novel optical modulation scheme that meets the optical communications requirements. The proposed odd clipping optical OFDM technique (OCO-OFDM) is based on the Fourier transform symmetry properties in which the imaginary and odd signal is converted to odd and real valued signal. As a result of this work, the proposed OCO-OFDM and its modified version have several benefits over ACO-OFDM and DCO-OFDM. By introducing a better bit error rate, with the same spectral efficiency as DCO-OFDM and the same power efficiency as ACO-OFDM for real valued modulation technique as Binary Phase-Shift Keying (BPSK), and with the same spectral efficiency and power efficiency as ACO-OFDM for complex valued modulation technique as Quadrature Phase-Shift Keying (QPSK) and Eight Phase-Shift Keying (8PSK).