Let F be a field with 2 = 0 and φ =¿ a1, . . . , an À an n-fold anisotropic bilinear Pfister form over F with function field F (φ). In this paper we compute ker[In F /I n+1 F → In F (φ)/I n+1 F (φ)] where IF ⊂ W (F ) is the maximal ideal in the Witt ring W (F ) of F . We use this computation to prove a n-linkage property of the subfields F (a1, . . . , an).