  The difference between slice and doubly-slice knots is reflected in algebra
by the difference between metabolic and hyperbolic Blanchfield linking forms.
We exploit this algebraic distinction to refine the classical Witt group of
linking forms by defining a `double Witt group' of linking forms. We calculate
the double Witt group for Dedekind domains and precisely determine its
relationship to the classical Witt group. Finally, we prove that the double
Witt group of Seifert forms is isomorphic to the double Witt group of
Blanchfield forms.
