Crystals of Ce-doped SrMgF4, strontium magnesium tetrafluoride, have been found to have a monoclinic P2(1) structure with doubled a and tripled c cell lengths compared with the orthorhombic Cmcm structure previously reported in the literature. The perovskite-type slabs, composed of corner-sharing MgF6 octahedra and Sr atoms, are stacked along the b axis. The six crystallographically independent MgF6 octahedra are rotated so as to provide long periodicities along a and c. The coordination numbers and bond distances around the six crystallographically independent Sr atoms are slightly different in each case. In the superstructure, the Sr atoms lie on local mirror planes which are thought to originate at the high-temperature phase transition.