We show how the proof of the Grothendieck Theorem for jointly completely
bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in
such a way that the method of proof is essentially C*-algebraic. To this
purpose, we use Cuntz algebras rather than type III factors. Furthermore, we
show that the best constant in Blecher's inequality is strictly greater than
one.Comment: 9 pages, minor change
