  We show that the motion on the n-dimensional ellipsoid is complete integrable
by exhibiting n integrals in involution. The system is separable at classical
and quantum level, the separation of classical variables being realized by the
inverse of the momentum map. This system is a generic one in a new class of
n-dimensional complete integrable Hamiltonians defined by an arbitrary function
f(q,p) invertible with respect to momentum p and rational in the coordinate q.
