Fe/NiO/Fe/CoO/Ag(001) single crystalline films were grown epitaxially and investigated by x-ray magnetic circular dichroism and x-ray magnetic linear dichroism. The bottom Fe layer magnetization is pinned through exchange coupling to the CoO layer and the top Fe layer magnetization can be rotated by an in-plane external magnetic field. We find that the NiO spins wind up to form a domain wall due to the perpendicular NiO/Fe interfacial coupling as the top layer Fe magnetization rotates from 0° to 90°, but switch wall chirality and unwind the wall as the Fe magnetization rotates from 90° to 180°. This observation shows that Mauri's 180° domain wall does not exist in perpendicularly coupled ferromagnetic-antiferromagnetic systems in the strong coupling regime.