  The aim of this paper is to give an explicit formula for the calculation of
the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the
index appearing in Gutzwiller's trace formula with a non-trivial extension of
the Conley--Zehnder index. This index can be related to the usual Maslov index
using the theory of the metaplectic group and the formalism of the
Arnol'd--Leray--Maslov index developed in previous work, and is extended to
symplectic paths with arbitrary endpoint.
