  Let $X$ be a smooth projective hypersurface of dimension $\geq 5$ and let $E$
be an arithmetically Cohen-Macaulay bundle on $X$ of any rank. We prove that
$E$ splits as a direct sum of line bundles if and only if $H^i_*(X, \wedge^2 E)
= 0$ for $i = 1,2,3,4$. As a corollary this result proves a conjecture of
Buchweitz, Greuel and Schreyer for the case of rank 3 arithmetically
Cohen-Macaulay bundles.
