  Following Ellis, we investigate the notion of totally free crossed squares
and related square complexes. It is shown how to interpret the information in a
free simplicial group given with a choice of CW-basis, in terms of the data for
a totally free crossed square. Results of Ellis then apply to give a
description in terms of tensor products of crossed modules. The paper ends with
a purely algebraic derivation of a result of Brown and Loday.
