A new series of computer simulations on a fluid of pseudo-hard bodies has been conducted in order to find a closed analytical expression for the direct correlation function as a function of the intermolecular distance and fluid density, in analogy with a similar expression for the fluid of hard spheres. A pseudo-hard body resulting from the extended primitive model of water has been considered. The accuracy of the expression has been tested against computer simulation results for pair correlation function and pressure of the system and turned out to be fairly high. The direct correlation function is important for the construction of weighted density functionals, and consequently any other theoretical study of the properties of inhomogeneous systems containing associating component.