We have calculated the relativistic corrections to the diamagnetic term of the nuclear magnetic shielding constants for a series of molecules containing heavy atoms. An analysis of the contributions from localized orbitals is performed. We establish quantitatively the relative importance of inner core and valence shell molecular orbitals in each correcting term. Contributions from the latter are much less important than those from the former. The calculated values of the correction sigma(L-PSO), first derived within the linear response elimination of small component formalism, show a power-law dependence on the nuclear charge approximately Z(3.5), in contrast with the approximately Z(3.1) behavior of the mass-velocity external-field correction to the paramagnetic term previously reported.