A new cost-effective approach and computational program POLMAG-3 for performing ab initio calculations of molecular magnetic susceptibility have been developed within the framework of the coupled perturbed Hartree-Fock approach based upon the simultaneous analytical dependence of both the bond order matrix and basis set functions on the corresponding perturbation parameters. The test calculations performed for a series of molecules within the proposed approach with the 6-31G basis set show good agreement with experiments.