Centers of generic algebras with involution

Let F be an infinite field of characteristic different from 2. Let n be a positive integer, and let V=Mn(F)⊕Mn(F). The projective symplectic and orthogonal groups, PSpn and POn, act on V by simultaneous conjugation. Results of Procesi and Rowen have shown that F(V)PSpn and F(V)POn are the centers of the generic division algebras with symplectic and orthogonal involutions, respectively. Saltman has shown that F(V)PSpn and F(V)POn are stably isomorphic over F for all n even, and that for all n odd F(V)POn is stably rational over F. Saltman has also shown that for all n for which the highest power of 2 dividing n is less than 8, F(V)PSpn and therefore F(V)POn are stably rational over F. We show that the result is also true for all n for which the highest power of 2 dividing n is 8.