  In this paper, we consider the reducibility of the quasi-periodic linear
Hamiltonian system $$\dot{x}=(A+\varepsilon Q(t))x, $$ where $A$ is a constant
matrix with possible multiple eigenvalues, $Q(t)$ is analytic quasi-periodic
with respect to $t$, and $\varepsilon$ is a sufficiently small parameter. Under
some non-resonant conditions, it is proved that, for most sufficiently small
$\varepsilon$, the Hamiltonian system can be reduced to a constant coefficient
Hamiltonian system by means of a quasi-periodic symplectic change of variables
with the same basic frequencies as $Q(t)$. Application to quasi-periodic Hill's
equation is also given.
