  In this paper we first establish the relation between the zeta-determinant of
a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary
condition on a cylinder. Using this result and the gluing formula of the
zeta-determinant given by Burghelea, Friedlander and Kappeler with some
assumptions, we prove the adiabatic decomposition theorem of the
zeta-determinant of a Dirac Laplacian. This result was originally proved by J.
Park and K. Wojciechowski in [11] but our method is completely different from
the one they presented.
