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In this paper we consider user scheduling problem for linearly preceded multiuser multiple-input multiple-output (MIMO) downlink, where base station as well as the mobile receivers are equipped with multiple antennas. Optimal precoding involves dirty paper coding (DPC) technique, and it is highly nonlinear and complex. On the other hand, complete inter-user interference cancellation using linear zero-forcing or block diagonalization precoding are suboptimal. Hence, we consider successive zero-forcing precoding, which achieves improved system throughput compared to block diagonalization by allowing users to work under limited interference. Due to the dimensionality constraint of linear precoding techniques user scheduling is required. The optimal user scheduling involves exhaustive search, which becomes very complex for realistic numbers of users and transmit antennas. In addition, for successive zero-forcing precoding the order in which users are precoded successively is important for sum rate maximization, which further increases the complexity of exhaustive search. In this paper we develop a low complexity greedy user scheduling algorithm for successive zero-forcing precoding, which incorporates various user ordering techniques. Simplified heuristic scheduling metrics are proposed, which are shown to perform close to the exhaustive search method. A suboptimal user ordering technique that is similar to the order, in which the proposed greedy user selection selects users, is proposed. Further simplification of regular greedy scheduling algorithm is obtained with the proposed intermediate user grouping technique. The proposed algorithm is of low complexity, but provides performance close to the highly complex exhaustive search algorithm.