Simultaneous transmission to multiple users using orthogonal beamforming, known as space-division multiple-access (SDMA), is capable of achieving very high throughput in multiple-input multiple-output (MIMO) broadcast channel. In this paper, we propose a new orthogonal beamforming algorithm to achieve high capacity performance in MIMO broadcast channel. In the proposed algorithm, the base station generates a unitary beamforming vector set using Gram-Schmidt orthogonalization. We extend the algorithm of LF-OSDMA (Opportunistic SDMA with Limited Feedback) to guarantee that the system never loses multiplexing gain for fair comparison with the proposed algorithm by informing unallocated beams. Finally, we show that the proposed method can achieve a significantly higher sum capacity than LF-OSDMA and the extended LF-OSDMA without a large increase in the amount of feedback bits and latency.