Dawn-dusk traversals of the auroral zone by the German polar orbiting satellite Azur are used to reexamine the previously reported dawn-dusk asymmetry of the boundary position of the 40-keV electrons. This asymmetry, i.e., higher latitudes of the boundary positions in the dawn sector than in the dusk sector, disappears during prolonged periods of low electrojet activity. Symmetric boundary positions, i.e., significantly lower than average boundary positions in the dawn sector, are found whenever the electron flux decreases smoothly to the cosmic ray background over the polar cap and when there is no enhanced precipitation. Similar, undisturbed flux profiles observed by Ogo 6 at E>30keV are used to extend the study to all local times. The resulting average boundary contour has an almost circular shape, centered at 2¿ away from the magnetic pole on the midnight meridian and is compared with the average position of quiet auroral arcs and also with the average pattern of field-aligned currents for AL<100nT. The average boundary contour of undisturbed 30- and 40-keV electron flux profiles is interpreted as the high-latitude limit of stable trapping in the undisturbed magnetosphere.