Resistivity, specific heat and magnetization measurements on the shape memory compound Co₂NbSn corroborate the presence of ferromagnetic order below 119 K and a structural phase transition at 235 K. High-resolution neutron powder diffraction measurements confirmed that the high-temperature cubic phase has the Heusler L2₁ structure and established that the low-temperature phase is orthorhombic with space group Pmma. The thermal variation of the specific heat at low temperatures indicates a high density of states consistent with electronic structure calculations and a band Jahn-Teller mechanism for the transformation.