At a material point of a hyperelastic anisotropic body the strain and
the stress tensors do not share, in general, a common basis of proper
vectors. It is shown that there are at least three rotations which, wh
en applied to the reference configuration before a given deformation,
yield a pair of coaxial strain and stress tensors. This is an improvem
ent on a previous result, which showed such rotations to be no fewer t
han two. The proof is based on the application of Milnor's theorem fro
m differential topology.