  A {\em complex} canonical transformation is found that takes the fourth order
derivative Pais-Uhlenbeck oscillator into two independent harmonic oscillators
thus showing that this model has energy bounded from below, unitary
time-evolution and no negative norm states, or ghosts. Such transformation
yields a positive definite inner product consistent with reality conditions in
the Hilbert space. The method is illustrated by eliminating the negative norm
states in a complex oscillator. Extensions to other higher order mechanical
models and field theory are discussed.
