The "enhanced Milnor number" of a fibered link was introduced homotopy theoretically in [N-R I] . We recall its definition later. It lies in Z(~Z or Z(~(Z/2) according as the ambient dimension is 3 or greater than 3. Its first component is, up to sign, the usual Milnor number, which is the dimension of the Seifert form if the fibered link is simple. We will see that for simple fibered links in high dimensions the whole enhanced Milnor number is an invariant of the Seifert form. In fact, the main contributions of this paper can be phrased as follows (the concepts involved in these results are recalled below).