We present a simple Onsager type density functional theory (DFT) of a two-dimensional system of hard needles and assume that it can be applied to describe intensive and short range properties of a real system which, on the other hand, on larger scales exhibits topological order. It is shown that the transition point of the isotropic-nematic transformation and the state equation obtained are almost the same as those predicted from the computer simulations [ Phys. Rev.  A31, 1776 (1985)] for small and undistorted system, which is never the case in liquid crystals, where these results are shifted in the density and require rescalings like, for instance, the Parson--Lee approach  Phys. Rev.  A19, 1225 (1979);  J. Chem. Phys.  87, 4972 (1987);  J. Chem. Phys. 89, 7036 (1988). Similar effect occurs for the chemical potential. Such behavior is attributed to the presence of negative values of higher virial coefficients, which may cancel the influence of the other positive coefficients in such a way that the second virial approximation gives accurate predictions. The above conclusion coincides with the Onsager idea that the second virial DFT theory for infinitely 3D hard particles is accurate. We notice that this coincidence comes from the fact that the 3D and 2D interaction models are governed by the same theoretical formulation. We also claim that the observed in the Monte Carlo simulation the disclinations unbinding process does not mean the change from the isotropic to the nematic phase (IN), as believed before, since the spontaneously drifting disclinations cannot be responsible for the changes of the system symmetry. The IN transition, as usual, is driven by the molecular interactions and the disclination unbinding must undergo then in the uniaxial phase. We also confirm that the chemical potential has a smooth character as a function of pressure, whereas it has an abrupt change in the slope at the point of transition while plotted  versus density.

PACS numbers: 71.15.Mb, 64.70.Md, 61.30.--v