  Maslov indices in periodic-orbit theory are investigated using phase space
path integral. Based on the observation that the Maslov index is the
multi-valued function of the monodromy matrix, we introduce a generalized
monodromy matrix in the universal covering space of the symplectic group and
show that this index is uniquely determined in this space. The stability of the
orbit is shown to determine the parity of the index, and a formula for the
index of the n-repetition of the orbit is derived.
