We study the ionospheric convection that prevails during the passage of a magnetic cloud past the Earth. For the cloud studied here, January 13‐15, 1988, the ionospheric convection was measured almost continually in cross sections of the polar cap and auroral zone by the Defense Meteorological Satellite Program (DMSP) polar‐orbiting satellite. In turn, the conditions in the magnetic cloud are like those of a controlled laboratory experiment: First, the magnetic field changes smoothly and slowly on time scales much longer than the expected ionospheric response time, ensuring that the external interplanetary conditions giving rise to any ionospheric flow pattern are known to unprecedented accuracy. Second, over the longer time scale of the magnetic cloud passage, the magnetic field vector rotates by over 180° such that the magnetic cloud divides into two intervals of northward (Bz > 0) and southward (Bz < 0) pointing interplanetary magnetic field (IMF) of 11 and 18 hours duration, respectively. During the former interval our observations show that (1) for strongly northward IMF (Bz > 18 nT) the convection in one (the southern) hemisphere is characterized by a two‐cell convection pattern confined to high latitudes (≥ 75°) with sunward flow over the pole (“reverse” two‐cell convection). (2) The strength of the flows (∼1 km/s) is comparable to that seen under southward IMF later. (3) Superimposed on this convection pattern there are clear dawn‐dusk asymmetries associated with a one‐cell convection component whose sense depends on the polarity of the magnetic cloud's large east‐west magnetic field component. (4) Whilst the flows in the southern hemisphere are ordered into a well‐defined convection pattern, the flows in the northern hemisphere are very irregular, varying on short spatial scales. When the cloud's magnetic field turns southward the following observations were made: (1) The convection is characterized by a two‐cell pattern extending to lower latitudes (∼50°) with antisunward flow over the pole (“standard” two‐cell convection). (2) There is no evident interhemisphere difference in the structure and strength of the convection. (3) Superimposed dawn‐dusk asymmetries in the flow pattern are observed which are only in part attributable to the east‐west component of the magnetic field. (4) A dawn‐dusk asymmetry in the latitude of the convection reversal boundary also exists, which is most pronounced in the northern hemisphere (up to 10° difference). We study the transition from a reverse to standard two‐cell convection pattern and find that because of the large By component of the magnetic field inside the magnetic cloud, this transition actually takes place before the external field turns southward. It occurs when the magnetic shear angle between the subsolar magnetospheric field and the magnetic field of the magnetic cloud is ∼70°. We consider the effect of the Bz component of the cloud magnetic field on the size of the open field line region or polar cap, inferred from the convection pattern. We argue that the long‐term variation in the polar cap size is determined by the temporal gradient of the Bz component. We investigate the strength of the ionospheric convection, parameterized by the maximum potential difference across the convection pattern, as a function of the Bz component of the cloud magnetic field, extending the range of similar investigations. For strongly northward IMF a potential difference of 60‐80 kV is observed across the reverse two‐cell convection pattern. For southward IMF the potential difference across the standard two‐cell convection pattern changes almost linearly with Bz, attaining its maximum value of ∼180 kV at the extreme value of Bz = −19 nT reached in this cloud.