This study considers successive orthogonal beamforming (SOBF) for multicell downlink transmissions. A group of base stations (BSs) are in cooperation for effective downlink transmissions to cell-edge users, which is usually referred to as cooperative multi-point. As the number of cell-edge users is small and varying, conventional beamforming schemes, for example, zero-forcing beamforming (ZFBF), are not suitable for the multicell scenario. In the SOBF scheme considered here, the beamforming vectors are found in a successive manner when a new user comes in, so that the beamforming vectors of the existing users remain unchanged. With limited channel state information at the group of BSs, a new successive beam allocation (SBA) scheme is proposed for SOBF. In SBA, the candidate beams are broadcasted to all the users through downlink before the index of the best beam is sent back to the BS by each user. The sum rate performance of a system with two users is studied analytically. The numerical results are presented to show that the proposed SOBF with SBA outperforms ZFBF with conventional feedback strategy.