Eigenvector matrices of Cartan matrices for finite groups

Let CB be the Cartan matrix of a p-block B of a finite group G. We show that there is a unimodular eigenvector matrix UB of CB over a discrete valuation ring R, if all eigenvalues of CB are integers when B is a cyclic block, a tame block, a p-block of a p-solvable group or the principal 3-block with elementary abelian defect group of order 9.