We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.