A preliminary study is made of a two-dimensional model of an imperfect gas of `attracting rigid squares' which is a limiting case of the two-dimensional Ising model with second-nearest neighbour interactions studied by Domb and Potts. The qualitative behaviour of the high order Mayer cluster-sums is determined by a method used by Temperley. It is found that at high temperatures these sums alternate in sign, which is what would be expected if the approaching transition were the formation of an ordered structure. As we lower the temperature, the analytic behaviour of the cluster-sums progressively changes to what was found by Yang and Lee when the approaching transition involves the formation of large domains, analogous to liquefaction.It is tenatively concluded that this version of the Ising model may show two transitions below a certain critical temperature, just like a real imperfect gas.