  For an integrable Hamiltonian $H_0=1/2\sum_{i=1}^dy_i^2$ $(d\geq 2)$, we show
that any Lagrangian torus with a given unique rotation vector can be destructed
by arbitrarily $C^{2d-\delta}$-small perturbations. In contrast with it, it has
been shown that KAM torus with constant type frequency persists under
$C^{2d+\delta}$-small perturbations.
