We introduce a method for obtaining atomic point-charges that yield accurate representations of the electrostatic potentials (ESP) of large systems. The method relies on a decomposition of the density and subsequent projection of the multipole moments of the density components onto neighbouring atomic sites. The resulting local multipole-derived charges (LMDCs) are well-defined, do not require sampling of the ESP at grid points around the molecule and provide a good description of the electrostatic potential. This local approach circumvents the numerical problems that arose in our original method which was designed to find the optimal atomic charge representation of the ESP of a system outside the electron density.