Abstract 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 method, the base station generates a unitary beamforming vector set using Gram-Schmidt orthogonalization. We extend the algorithm of opportunistic SDMA with limited feedback (LF-OSDMA) to guarantee that the system never loses multiplexing gain for fair comparison with the proposed method by informing unallocated beams. 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.