For any n > 2, we construct central division algebras of exponent 2 and index 2n
 over a field E, which are indecomposable over any odd degree extension of E and
    which are sums of n + 1 quaternion algebras in the Brauer group of E. The
  construction also allows to prove that any multiquadratic extension of degree
   2^(n-1) over a field K becomes nonexcellent (in the sense of the theory of
       quadratic forms) when K is replaced by a suitable field extension.