By a mathematical analysis of the formulae of a quasi-crystalline model of liquids, i.e. a crystal lattice with smeared out lattice sites, it is shown that this model leads to a nonphysical asymptotic behaviour of the radial distribution function. To remove this defect it is necessary to modify the initial lattice by changing either the coordination numbers or the radii of the coordination spheres. Some ways of such modification are given and illustrated by concrete calculations.