  A link L in the 3-sphere is called Brunnian if every proper sublink of L is
trivial. In a previous paper, the first author proved that the restriction to
Brunnian links of any Goussarov-Vassiliev finite type invariant of
(n+1)-component links of degree<2n is trivial. The purpose of this paper is to
study the first nontrivial case. We will show that the restriction of an
invariant of degree 2n to (n+1)-component Brunnian links can be expressed as a
quadratic form on the Milnor link-homotopy invariants of length n+1.
