Let A be a completely contractive Banach algebra.  For any index set I we consider the space of bounded I X I-matrices with entries in A.  Under Schur multiplication, this space of matrices is itself a completely contractive Banach algebra. In particular, for any locally compact group, we obtain natural operator-valued Fourier-Stieltjes and measure algebras. This is joint work with G. A. Bagheri-Bardi and A. R. Medghalchi.