In this paper, we propose two power randomization schemes for the random beamforming (RBF) based MIMO systems in cellular downlink. In the proposed system, a BS randomizes not only the pre-coding matrix but also the power allocation matrix, while the conventional RBF system allocates an equal power to each transmit stream. The proposed water-filling based power randomization scheme (Scheme-I) is proper in the low SNR values and the proposed random-power based randomization scheme (Scheme-II) is proper in the high SNR values. The proposed system with the power randomization outperforms the conventional RBF system which allocates the same power for each data stream.