A structural transition with a reduction in symmetry of the high temperature cubic phase (sp. gr. Fd3m) to the tetragonal phase (sp. gr. I4₁/amd) and the appearance of a ferrimagnetic structure occur in CuFe₂O₄ copper ferrite at T ≈ 440°C. It is established by an experiment on a high-resolution neutron diffractometer that the temperature at which long-range magnetic order occurs is higher than that of tetragonal phase formation. When cooling CuFe₂O₄ spinel from 500°C, the equilibrium coexistence of both phases is observed in a fairly wide temperature range (∼40°C). The composition studied is a completely inverse spinel in the cubic phase, and in the tetragonal phase the inversion parameter does not exceed few percent (x = 0.06 ± 0.04). At the same time, the phase formed upon cooling has a classical value of tetragonal distortion (γ ≈ 1.06). The character of temperature changes in the structural parameters during the transition from cubic to tetragonal phase indicates that this transition is based on the Jahn-Teller distortion of (Cu,Fe)O₆ octahedra rather than the mutual migration of copper and iron atoms.