We propose a new method for generating a peak cancellation (PC) signal vector considering the variance in the average signal power among transmitter antennas in the peak-to-average power ratio (PAPR) reduction method for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) signals using the null space in a MIMO channel. We first analyze the conditions for the PC signal vector to achieve a sufficient PAPR reduction effect after its projection onto the null space. The analysis indicates that the PC signal vector should be uncorrelated with the transmission signal vector as much as possible. Based on the analysis and the fact that reducing the difference in the average signal power among the transmitter antennas is beneficial for PAPR reduction, we propose a new method for generating a PC signal vector. The proposed PC signal vector is designed so that at the target timing, the signal power levels of all the transmitter antennas are restricted to be below the maximum power threshold while also being above the minimum power threshold. The newly introduced feature, i.e., controlling the signal power to be above the minimum power threshold, contributes to reducing the transmission power variance among antennas and increasing the PAPR reduction effect after the projection of the PC signal onto the null space in the MIMO channel. This is accomplished by reducing the correlation between the PC signal and data signal vectors. Computer simulation results show that the proposed method provides superior PAPR reduction characteristics compared to those for the conventional method.