  Path integrals developed by Richard Feynman have been an important tool in
Physics in studying quantum field theory. In mathematics, it has also been
widely used in providing formal proofs in the study of Index theorem and
asymptotic behaviors of heat kernels. Finite dimensional approximations to path
integral representations give a way to interpret path integrals and make the
formal argument rigorous. The central idea is to restrict a path integral to
smaller path spaces where everything is well defined and then to interpret the
original path integral as a "limit" when smaller path spaces "exhaust" the full
path space (Wiener space). In this paper I will present a finite dimensional
approximation to Brownian bridge on a symmetric space of non---compact type
using pinned piecewise geodesic space adapted to partitions of time.
