A novel modulation technique coined U-OFDM is proposed. U-OFDM uses different time sample states and an innovative rearrangement of the Orthogonal Frequency Division Multiplexing (OFDM) frame which allow for the creation of unipolar OFDM signals required for Optical Wireless Communication (OWC) with Light Emitting Diodes (LEDs). In comparison to similar techniques like DC-biased Optical OFDM (DCO-OFDM) and Asymmetrically Clipped Optical OFDM (ACO-OFDM), U-OFDM is both optically and electrically more power efficient in an Additive White Gaussian Noise (AWGN) channel, which is prevalent in an optical wireless system.