  A generalized canonical form of action of dynamic theories with higher
derivatives is proposed, which does not require the introduction of additional
dynamic variables. This form is the initial point for the construction of
quantum theory, in which the state of motion of the system is described by the
wave functional on its trajectories in the configuration space, and the
functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck
oscillator is considered as the simplest model. For this case, the
correspondence between the new form of quantum theory and "ordinary" quantum
mechanics has been established in the local limit, when the Pais-Uhlenbeck
oscillator is reduced to the "ordinary" harmonic oscillator.
