Intelligent reflecting surface (IRS) has become a promising technology to aid next generation wireless communication systems. In this paper, we develop an alternating beamforming technique with a novel concept of IRS element allocation for multiple-input multiple-output systems when a base station supports multiple single antenna users aided with a single IRS. Specifically, we allocate each IRS element separately to each user, thus, in the beamforming stage allowing the IRS element only consider a single user at a time. In result to this separation, the complexity is vastly decreased. The proposed beamforming technique tries to maximize the minimum rate of all users with minimal complexity. In the numerical results, we show that the proposed technique is comparable to the convex optimization-based benchmark with sufficiently less complexity.