  We refine the Whitehead torsion of a chain equivalence of finite chain
complexes in an additive category $\bA$ from an element of
$\widetilde{K}^{iso}_1(\bA)$ to an element of the absolute group
$K_1^{iso}(\bA)$. We apply this invariant to symmetric Poincar\'e complexes and
identify it in terms of more traditional invariants. In the companion paper [1]
(joint with Ian Hambleton and Andrew Ranicki) this new invariant is applied to
obtain the multiplicativity of the signature of fibre bundles mod 4.
