The beamforming weights which can suppress the interfering signal toward out-of-cell mobile stations in downlink are designed for a time division duplexing based OFDMA system when the channel information is not perfect. The derived beamforming weights do not improve the average SINR performance monotonously with the increased transmit SNR if the inverse of the transmit SNR is used as the regularization factor of the beamforming weights and the channel information obtained by the BS to design the BF weights is not perfect. Therefore, we suggest a simple scheme to select the regularization factor. The proposed beamforming weights improve the performance monotonously with the increased transmit SNR and achieve near-optimal performance. The performance achieved by applying the beamforming weights used in uplink to downlink beamforming is also investigated.