  We consider the Schr\"odinger equation $ih\partial_t\psi = H\psi$,
$\psi=\psi(\cdot,t)\in L^2({\mathbb T})$. The operator $H = -\partial^2_x +
V(x,t)$ includes smooth potential $V$, which is assumed to be time
$T$-periodic. Let $W=W(t)$ be the fundamental solution of this linear ODE
system on $L^2({\mathbb T})$. Then according to terminology from
Lyapunov-Floquet theory, ${\cal M}=W(T)$ is the monodromy operator. We prove
that ${\cal M}$ is unitarily conjugated to $\exp\big(-\frac{T}{ih}
\partial^2_x\big) + {\cal C}$, where ${\cal C}$ is a compact operator with an
arbitrarily small norm.
