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The structure of the tetragonal phase of the A-site-substituted perovskite sodium bismuth titanate, Na0.5Bi0.5TiO3, has been determined by neutron powder diffraction at 698 K. The structure was refined in space group P4bm with a (= b) = 5.5191 (1), c = 3.9085 (1) Å, V = 119.055 (5) Å3, Z = 2 and Dx = 5.91 Mg m−3. The structure exhibits an unusual combination of in-phase (a0a0c+) tilts and antiparallel cation displacements along the polar c axis, which results in a new variant of the perovskite structure.