A novel methodology of transmit beamforming for systems subjected to equivalent isotropic radiated power restrictions is presented in this paper. Based on the properties of the radiation due to the optimal beamforming method compared with that due to the eigen-beamforming, beamforming vectors are designed by perturbing the scaled eigen-beamforming vector such that the peak-to-average power ratio of the spatial radiation is reduced. Two algorithms incorporating this general methodology are presented. With a computational complexity less than the optimal method, both are shown to outperform conventional suboptimal beamforming methods. For example, in an investigated system with four transmit and one receive antennas, performance is improved by more than 1 dB at a packet-error-rate of 10(-3).