Multiuser diversity is achieved by maximum C/I scheduler in both fast and slow fading scenarios. However, fairness among multiple users is not guaranteed in slow fading channel because time and frequency resource are always occupied by the user with largest signal to interference and noise ratio(SINR). Opportunistic beamforming using dumb antennas is a multiple antennas transmit technique to increase the fluctuation rate and dynamic range of effective channel coefficients in slow fading environment. In this paper, we propose a method to improve the fairness of maximum C/I scheduler with the technique of dumb antennas. The theoretical analysis of users' scheduling probability shows that the fairness of maximum C/I scheduler can be greatly improved by dumb antennas in slow fading channels without significant loss in cell spectrum efficiency. The engineering issues of its application in the downlink transmission of 3GPP LTE system are discussed. The numerical results of simulation with practical LTE configurations and assumptions also verify our proposal.