A search for fast flows in the plasma sheet during quiet times was conducted in order to further test the previously found close association between fast flows and auroral brightenings. We first identified quiet intervals of at least 30-min duration in the Polar ultraviolet global images of auroras. During 16 months of Polar observations from January 1997 through April 1998, 41 quiet intervals were identified when Geotail was between 8 and 31 RE down the tail and within 10 RE of the midnight meridian. Fast flows were more rare during the quiet intervals than at other times. For 4 of the 41 intervals identified, Geotail detected flows faster than 300 km s-1 in the plasma sheet. All the four flows were earthward parallel flows accompanied by northward magnetic field beyond 20 RE, and there were no perpendicular flows faster than 300 km s-1. To understand the nature of the fast (but not perpendicular) flows during the quiet intervals, an earthward flow at 21 RE down the tail was studied in detail. The plasma beta was higher than unity during the earthward flow, but the fastest ion velocity moments consisted of the two counterstreaming components flowing along the magnetic field, a characteristic known to define the plasma sheet boundary layer. Our results further support the close association between auroral brightenings and clear fast flows as seen in previous studies, because no perpendicular fast flows were found during quiet intervals. Since some perpendicular flows slower than 300 km s-1 were found beyond ~20 RE down the tail, a velocity of ~300 km s-1 appears to statistically make a difference in the geoeffectiveness of perpendicular flows.