System of hard squares in two dimensions (2D) has been studied by Monte Carlo simulations. The simulations indicate that the isotropic fluid phase in this system does not freeze into a 2D 'crystalline' phase (of square lattice and quasi-long-range translational order) but transforms into an intermediate phase with the quadratic quasi-long-range orientational order (of coupled molecular axes and intermolecular bonds) and the translational order decaying faster than algebraically. The equation of state and the specific heat of the system are surprisingly well reproduced by smoothed version of the free volume theory in the whole density range.
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