A novel procedure for calculating magnetic susceptibilities and nuclear magneticshieldings in molecules is outlined, based on formal annihilation of transverseparamagnetic contribution to quantum mechanical current density induced within theelectron cloud by an external homogeneous, static magnetic field. Within this method allthe components of nuclear magnetic shielding are independent of a gauge translation, inany calculation relying on the algebraic approximation, irrespective of size and quality ofthe gaugeless basis set adopted; magnetic susceptibilities are invariant for centersymmetricmolecules (virtual invariance is actually observed for molecules of arbitrarysymmetry). Large basis set calculations of near-Hartree-Fock magnetic prop...