  The odd signature operator is a Dirac operator which acts on the space of
differential forms of all degrees and whose square is the usual Laplacian. We
extend the result of [15] to prove the gluing formula of the zeta-determinants
of Laplacians acting on differential forms of all degrees with respect to the
boundary conditions ${\mathcal P}_{-, {\mathcal L}_{0}}$, ${\mathcal P}_{+,
{\mathcal L}_{1}}$. We next consider a double of de Rham complexes consisting
of differential forms of all degrees with the absolute and relative boundary
conditions. Using a similar method, we prove the gluing formula of the
zeta-determinants of Laplacians acting on differential forms of all degrees
with respect to the absolute and relative boundary conditions.
