  Let p: M -> B be a family of compact manifolds equipped with a unitarily flat
vector bundle F -> M. We generalize Igusa's higher Franz-Reidemeister torsion
\tau(M/B;F) to the case that the fibre-wise cohomology H^*(M/B;F) -> B carries
a parallel metric. If moreover M admits a fibre-wise Morse function, we compute
the difference of \tau(M/B;F) and the higher analytic torsion \Cal T(M/B;F). We
also generalise the examples given in math.DG/0111222 .
