Let X be a smooth projective hypersurface of dimension ≥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,∧2E)=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. © 2017 Elsevier Inc.