The Lifschitz and Hameiri theory for short-wave instabilities is used to show that any steady inviscid plane flow subjected (or not) to a Coriolis with perpendicular angular velocity vector is unstable to three-dimensional perturbations if Φ(x0)<0 on a stagnation point located at x0. Φ is the second invariant of the inertial tensor [Leblanc and Cambon, Phys. Fluids 9, 1307 (1997)]. The particular cases of zero absolute W(x0)+2Ω=0 and zero tilting W(x0)+4Ω=0 vorticities are also considered. The criterion is applied to Chaplygin’s non-symmetric dipolar vortex moving along a circular path, which is shown to be unstable.