The signal to interference plus noise ratio (SINR) feedback has been utilized in random beamforming (RBF) to select users for the provision of service in multiple-input multiple-output (MIMO) systems. A large number of users are required to obtain the gain of multi-user diversity for a downlink transmission. However, if the number is not large enough, it may be difficult to obtain multi-user diversity, leading to a rapid degradation in performance. To resolve this problem, it is necessary to find beamforming matrix close to the channels of the selected users. In this paper, a beamforming matrix transformation for RBF (BMT-RBF) is presented, demonstrating an efficient search of random beams correlated with user channels as opposed to conventional ones, over a small number of users.