The structure of the spinel-type oxide CuRh2O4 has been determined between 25 and 650 degrees C using powder neutron diffraction methods. A first-order phase transition from a tetragonal to a cubic structure occurred at ca. 575 degrees C. The high-temperature cubic structure is a normal spinel (Fd(3) over bar m, a = 8.5487(2) Angstrom, x = 0.2601(4)), whereas at room temperature the structure can be described as a distorted spinel ((1)/amd, = 6.1707(4) Angstrom, c = 7.9183(7) Angstrom). In both forms, Cu and Rh exclusively occupy the tetrahedral and octahedral sites, respectively. The room temperature tetragonal distortion is ascribed to the strong preference of Cu2+ for a square planar geometry. From valence bond sum analysis, it was concluded that the transition is not electronic in origin.