Routine Super Dual Auroral Radar Network ionospheric plasma convection maps are used to study the structure of the near-noon convection established at small interplanetary magnetic field (IMF) Bz and By. During such intervals, the influence upon convection of the quasi-viscous processes at the magnetopause is expected to be at least as important as the effect of magnetic field line reconnection processes. It was found that, despite the small IMF Bz and By, there was a significant plasma flow across the noon meridian, so that the convection throat with the antisunward plasma flow was shifted toward earlier magnetic local times (to ~1100 magnetic local time). It was also found that the size and shape of the morning convection cell was similar to the size and shape of the evening cell. It is argued that the shift of the convection throat toward morning hours is most likely caused by the effects of the ionospheric polar cap plasma disconnection from corotation with the ionospheric plasma on closed magnetic field lines. Other possible causes for the observed asymmetry are discussed. ¿ 1998 American Geophysical Union