The phase diagram of lead-free piezoelectric KxNa1−xNbO3 has been studied, with particular focus on the proposed morphotropic phase boundaries, by powder and single crystal x-ray diffraction. The tilt system and cation displacement has been mapped out as a function of temperature and composition, highlighting changes in the oxygen octahedra at x=0.2 and x=0.4 at room temperature. The orthorhombic to monoclinic boundary at x=0.5 has been investigated, with a subtle change in the structure observed. The conclusion is that KxNa1−xNbO3 does not display a morphotropic phase boundary comparable with that in lead zirconate titanate, and that the most significant structural change as a function of composition occurs at x=0.2 because of the change of the tilt system.