In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system , where is a constant matrix with possible multiple eigenvalues, is analytic quasiperiodic with respect to , and is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small , the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as . Applications to the Schrödinger equation are also given.