To achieve a very high data rate within a limited frequency band in orthogonal frequency division multiplexing (OFDM) systems, multi-input multi-output (MIMO) techniques are very promising. Moreover, if a transmitter has the channel state information (CSI), the achievable spectrum efficiency can be maximized using the eigenbeam-space. division multiplexing (E-SDM). However, this scheme demands accurate channel estimation. Therefore, in a closed-loop transmission scheme, an increase in the amount of feedback is absolutely necessary for the E-SDM. This paper describes a downlink beamforming method that significantly reduces the amount of feedback needed by using the common transmission weight vectors in all sub-carriers, compared to the amount required for E-SDM. The proposed method also applies transmission diversity to compensate for the quality. The effectiveness of the proposed method was confirmed using computer simulations in both Ricean and Rayleigh fading environments.