Ionospheric convection over the southern polar cap on 11--12 May 1999 has been studied by using the Syowa East and South HF radar data and the DMSP ion driftmeter data, when the solar wind density was very low and geomagnetic activity was low. The overall convection pattern is consistent with the previous results by Ohtani et al. <2000>. However, the Syowa radars and the DMSP satellites observed very high (>1500 m/s) westward plasma flows at dusk directed from the nightside toward the dayside only in the Southern (dark) Hemisphere. The high-speed flow was observed continuously across the fields of view of both radars from 1530 UT on 11 May to 0200 UT on 12 May, when the solar wind density was close to minimum. Comparison with the DMSP particle and auroral image data shows that the westward flow regions were located in the middle of the auroral precipitation area. The strong asymmetry of the convection between the two hemispheres indicates the importance of the presence (absence) of solar illumination for the absence (presence) of the strong and localized ionospheric flows.