It is shown that the fluid branch of the hard square lattice gas terminates at a finite activity zf. Estimates of zf indicate that it is identical to the termination activity of the solid branch zs, found by Baxter, Enting, and Tsang [J. Stat. Phys. 22, 465 (1980)] to be at zs=3.7962(1), resulting in a second order phase transition with zf=zs=zc. The radius of convergence of the virial series p(ρ) is found to be smaller than the value of the critical density ρc. For a finite lattice a complex Yang–Lee zero of the grand partition function converges to zc like the reciprocal width of the lattice.