  The local Z_N quantized Berry phase for the SU(N) antiferromagnetic
Heisenberg spin model is formulated. This quantity, which is a generalization
of the local Z_2 Berry phase for SU(2) symmetry, has a direct correspondence to
the number of singlet pairs spanning on a particular bond, and is effective as
a tool to characterize and classify the various symmetry protected topological
phases of one-dimensional SU(N) spin systems. We extend the path-integral
quantum Monte Carlo method for the Z_2 Berry phase in order to calculate the ZN
Berry phase numerically. We demonstrate our method by calculating the Z_4 Berry
phase for the bond-alternating SU(4) antiferromagnetic Heisenberg chain, which
is represented by the Young diagram of four columns.
