In this paper, a novel method called offset modulation (OM-OFDM) is proposed, to control the peak-to-average power ratio of an OFDM signal. The theoretical bandwidth occupancy of the proposed offset modulated signal is derived. Using this bandwidth occupancy a closed form theoretical bit error rate (BER) expression for an offset modulated transmission is further derived, validated and compared to OFDM. Thereafter, the authors present a newly applied decision metric, which is used to compare the offset modulated method to the traditional OFDM transmission. After studying these results, OM-OFDM is shown to offer between 1.23 dB - 1.65 dB net performance gain at a BER of 10(-4) when compared to an OFDM transmission in frequency selective fading and additive white Gaussian noise channel conditions respectively.