A new method for the calculation of molecular magnetic susceptibility and nuclear magnetic shielding is presented. It is based on continuous transformations of origin of the current density which make the transverse part of the paramagnetic current vanish. For any molecule all the components of the nuclear magnetic shielding tensor provided by the new method are independent on the origin of the gauge, whereas the components of the magnetizability tensor are translationally invariant only for center-symmetric molecules (they, in general, show a linear dependence on the shift of origin). This method, termed CTOCD-PZ, has been implemented for the theoretical determination of molecular magnetic properties via numerical integration techniques and, from preliminar results obtained for methane and carbon dioxide molecules, reveals reliable.