An alternative approach for the calculation of the electron-positron (e-p) contribution to magnetic properties based on two-component Breit-Pauli spinors is presented. In it, the elimination of the small component scheme is applied to the inverse propagator matrix of e-p pairs. The effect of the positronic manifold is expressed as an operator acting on Breit-Pauli spinors. The operator form thus obtained sums up the relativistic correction as a geometric series and as a result a totally different behavior in the vicinity of a nucleus is obtained as compared to the one of the linear response approximation. This feature has deep influence in numerical values of the e-p contribution to the nuclear magnetic shielding of heavy atoms. Numerical calculations carried out for Kr, Xe, and I show that with this approach, the e-p contributions to this property are in good agreement with those of four-component methods.