  We have used neutron powder diffraction to solve the magnetic structure of
orthorhombic CoTi$_2$O$_5$, showing that the long-range ordered state below 26
K identified in our muon-spin rotation experiments is antiferromagnetic with
propagation vector ${\bf k}=(\pm \frac{1}{2}, \frac{1}{2}, 0)$ and moment of
2.72(1)$\mu_{\rm B}$ per Co$^{2+}$ ion. This long range magnetic order is
incompatible with the experimentally determined crystal structure because the
imposed symmetry completely frustrates the exchange coupling. We conclude that
the magnetic transition must therefore be associated with a spin Jahn-Teller
effect which lowers the structural symmetry and thereby relieves the
frustration. These results show that CoTi$_2$O$_5$ is a highly unusual low
symmetry material exhibiting a purely spin-driven lattice distortion critical
to the establishment of an ordered magnetic ground state.
