This study shows that, in cells with small thicknesses, the permanent polarization in the ferroelectric nematic phase of RM734 is aligned in the direction opposite to the rubbing direction. The electrode configuration induces an in-plane field near one substrate and a normal field near the other substrate. At low voltages, the permanent polarization rotates parallel to the substrate plane when its original orientation is at an angle with the electric field. The rotation occurs over a distance of more than 100 μm, where the applied electric field is very small. At higher voltages, the polarization aligns perpendicularly to the substrates under the influence of the transverse electric field. After removing the voltage, sometimes a slow reorientation of the polarization can be observed, which is ascribed to the slow release of ionic species. The results provide insight into the complex mechanisms that are involved in the switching of ferroelectric nematic liquid crystals.