This paper is concerned with the discrete Hamiltonian system
where and are real-valued functions defined on , the set of all integers, and denotes the forward difference operator defined by . The authors established several new Lyapunov-type inequalities for the above discrete linear Hamiltonian system when the end-points are not necessarily usual zeros, but rather, generalized zeros. These inequalities generalize and improve almost all related existing ones. By using these inequalities, an optimal stability criterion for discrete periodic linear Hamiltonian system is obtained.