We investigate the spatiotemporal variation of fault slip on the subduction interface in southwest Japan following the two 1996 Hyuganada earthquakes (M 6.7) using continuous GPS observations. A silent thrust slip event has been reported by Hirose et al. <1999>, following these earthquakes approximately 100 km to the north beneath the Bungo channel. We employ the Network Inversion Filter to rigorously invert for the fault slip distribution in space and time. The GPS time series is modeled as a sum of: (1) secular deformation; (2) coseismic station displacements; (3) transient fault slip; (4) random benchmark motion; (5) reference frame shifts; and (6) observational errors. Nonnegativity constraints effectively prohibit normal faulting on the subduction interface. Spatial and temporal smoothing parameters are estimated by the extended Kalman filter. The estimated fault slip-rate images postseismic slip following the two Hyuganada earthquakes. Slip associated with the silent thrust event began roughly 1 month after the second earthquake but initiated ~100 km to the northeast of the Hyuganada earthquakes. The slow event propagated southwest and downdip beneath the Bungo channel, lasting approximately 1 year with maximum slip-rates of 0.6 m/yr. The equivalent seismic moment was MW ~ 7.2. We can rule out the possibility that slip propagated from the source region of the Hyuganada earthquakes to the location of the silent earthquake. However, the timing of the events suggests a causal connection, perhaps due to static stress transfer. This kind of transient event, or silent earthquake, may reflect different fault zone characteristics and may be responsible for accommodating strain that would otherwise be released in large earthquakes.