The performance of multiuser multiple-input-multiple-output (MIMO) downlink systems with block diagonalization (BD) depends on the accuracy of the channel state information (CSI) available at the transmitter and the receiver. In time-varying channels, the CSI available at the transmitter (CSIT) is always outdated due to an inherent time delay between the uplink channel estimation and the downlink data transmission in time division duplexing (TDD) systems. This leads to a drastic degradation of system capacity. This paper first analyzes the effect of the outdated CSIT on multiuser MIMO downlink systems using the BD method and then proposes two linear processing methods, BD precoding with user selection and scheduling at the transmitter and total minimum mean squared error (MMSE) decoding at the receiver (TBDUSS-RTMMSE) and BD precoding at the transmitter with partial MMSE decoding at the receiver (TBD-RPMMSE), to mitigate the interference among data streams and users. Analysis and simulation re-sults show that these methods can effectively reduce the impairment of the outdated CSIT to increase the system sum capacity in a suitable time delay region of the CSIT.