  In this paper we are concerned with the periodic Hamiltonian system with one
degree of freedom, where the origin is a trivial solution. We assume that the
corresponding linearized system at the origin is elliptic, and the
characteristic exponents of the linearized system are $\pm i\omega$ with
$\omega$ be a Diophantine number, moreover if the system is formally
linearizable, then it is analytically linearizable. As a result, the origin is
always stable in the sense of Liapunov in this case.
