We have studied the hard-square lattice gas, using corner transfer matrices. In particular, we have obtained the first 24 terms of the high-density series for the order parameter p2 - pl. From these we estimate the critical activity to be 3.7962 _+ 0.0001. This is in excellent agreement with the earlier work of Gaunt and Fisher. It conflicts with the value 4.0 given by MiJller-Hartmann and Zittartz's formula for the critical point of the antiferromagnetic Ising model in a field, so we conclude that this formula, while a good approximation, is not exact.