We present superposed epoch analyses of the average ionospheric convection response in the northern and southern hemispheres to magnetospheric substorms occurring under different orientations of the interplanetary magnetic field (IMF). Observations of the ionospheric convection were provided by the Super Dual Auroral Radar Network (SuperDARN) and substorms were identified using the Far Ultraviolet (FUV) instrument on board the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) spacecraft. We find that during the substorm growth phase the expected IMF BY-dependent dawn-dusk asymmetry is observed over the entire convection pattern, but that during the expansion phase this asymmetry is retained only in the polar cap and dayside auroral zone. In the nightside auroral zone the convection is reordered according to the local substorm electrodynamics with any remaining dusk-dawn asymmetry being more closely related to the magnetic local time of substorm onset, itself only weakly governed by IMF BY. Owing to the preponderance of substorms occurring just prior to magnetic midnight, the substorm-asymmetry tends to be an azimuthal extension of the dusk convection cell across the midnight sector, a manifestation of the so-called ``Harang discontinuity.'' This results in the northern (southern) hemisphere nightside auroral convection during substorms generally resembling the expected pattern for negative (positive) IMF BY. When the preexisting convection pattern in the northern (southern) hemisphere is driven by positive (negative) IMF BY, the nightside auroral convection changes markedly over the course of the substorm to establish this same ``Harang'' configuration.