Abstract: We generalize Poincaré-Cartan integral invariant to a system with a singular higher-order Lagrangian which depends on time t explicitly, this invariant connected with the canonical equations and canonical transformation for the generalized constrained Hamiltonian system is studied. The connection between this invariant and Dirac's conjecture is discussed.An example shows that Dirac's conjecture fails for a system with a singular higher-order LagranJian.

Key words: higher-order derivative Lagrangian, Dirac's theory of constrained system, Poincaré-Cartan integral invariant