  We consider a Hamiltonian formulation of the (2n+1)-order generalization of
the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This
system is invariant under time translations. However, the corresponding Noether
integral of motion is unbounded from below and can be presented as a direct sum
of 2n one-dimensional harmonic oscillators with an alternating sign. If this
integral of motion plays a role of a Hamiltonian, a quantum theory of the
Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative
canonical formulation for the system under study to avoid this nasty feature.
