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In this paper, we investigate the multiuser diversity in the geometric mean decomposition-based multiple-input multiple-output (GMD-based MIMO) multiplexing system with one base station and a number of users. With time-varying fading, multiuser diversity is exploited by always allowing the base station to transmit to the user with their instantaneous SNR is near its own peak. The exact expressions of the bit error rate and capacity of the GMD-based single user MIMO multiplexing system in the downlink are presented. The multiuser average capacity obtained by scheduling is derived. By evaluating these expressions, we analytically show that, compared with the singular value decomposition-based MIMO (SVD-based MIMO) system, the GMD-based scheme make it rather convenient to design modulation and coding schemes for the subchannels when adaptive coding and modulation (ACM) are used. In addition, it is also shown that the multiuser average capacity of MIMO systems with small number of antennas can approach that with relative larger number of antennas when the number of scheduled users is sufficient large.