  We study quadratic forms on free modules with unique base, the situation that
arises in tropical algebra, and prove the analog of Witt's Cancellation
Theorem. Also, the tensor product of an indecomposable bilinear module $(U,
\gamma)$ with an indecomposable quadratic module $(V,q) $ is indecomposable,
with the exception of one case, where two indecomposable components arise.
