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