  Given two unitary involutions $\sigma_{1}$ and $\sigma_{2}$ satisfying $G
\sigma_{i} = - \sigma_{i} G$ on $ker B$ on a compact manifold with cylindrical
end, M. Lesch, K. Wojciechowski ([LW]) and W. M\"uller ([M]) established the
formula describing the difference of two eta-invariants with the APS boundary
conditions associated with $\sigma_{1}$ and $\sigma_{2}$. In this paper we
establish the analogous formula for the zeta-determinants of Dirac Laplacians.
For the proof of the result we use the Burghelea-Friedlander-Kappeler's gluing
formula for zeta-determinants and the scattering theory developed by W.
M\"uller in [M]. This result was also obtained independently by J. Park and K.
Wojciechowski ([PW2]).
