Schauder bases for symmetric tensor products

For a Banach space E with Schauder basis, we prove that the n fold symmetric tenser product (x) over cap (n)(mu,),E-s has a Schauder basis for all symmetric uniform crossnorms mu. This is done by modifying the square ordering on N-n and showing that the new ordering gives tensor product bases in both (x) over cap E-n(mu) and (x) over cap (n)(mu),E-s.