The paper develops a new technique to reduce the peak to average power ratio (PAPR) in OFDM modulation for a MIMO system. The proposed method exploits the eigen-beamforming mode (EM) in MIMO systems which is a common feature in 4th generation standards: WiMAX and LTE. These systems use the same beamforming weights for dedicated pilots and data so the weights are interpreted as a channel effect from the receiver perspective. There is no need to invert the weights at the receiver side since it is compensated for in channel equalization. Beamforming performance depends on the relative phase difference between antennas but is unaffected by a phase shift common to all antennas. In contrast, PAPR changes with the common phase shift. An effective optimization technique based on Sequential Quadratic Programming is proposed to compute the common phase shifts that minimize the PAPR.