  In this paper, we give the definition of Maslov-type index of the discrete
Hamiltonian system, and obtain the relation of Morse index and Maslov-type
index of the discrete Hamiltonian system which is a generalization of case
$\omega=1$ in \cite{RoS1}, \cite{RoS2} and \cite{Maz1} to case $\omega \in {\bf
U}$ via direct method which is different from that of \cite{RoS1}, \cite{RoS2}
and \cite{Maz1}. Moreover well-posedness of the splitting numbers $S_{\omega}$
of the discrete Hamiltonian system is proven, thus index iteration theories in
\cite{Bot1} and \cite{Lon4} are also valid for the discrete Hamiltonian system
case.
