For any n > 2, we construct central division algebras of exponent 2 and index 2^{n} 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.