  We present an example of an integrable Hamiltonian system with scalar
potential in the three-dimensional Euclidean space whose integrals of motion
are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger
equation cannot separate in any orthogonal coordinate system. This demonstrates
a loophole in the derivation of the list of quadratically integrable
Hamiltonian systems in [Makarov et al., A systematic search for nonrelativistic
systems with dynamical symmetries. Nuovo Cimento A Series 10, 52:1061-1084,
1967] where only separable systems were found, and the need for its revision.
