In the present article we have proposed and tested a new polarization scheme within the Schwinger Multichannel method based on a model potential to describe positron-molecule polarization and correlation. For this test, we have calculated integral and differential cross sections for the elastic scattering of positrons by pyrazine and compared these results with the existing theoretical and experimental data. Furthermore, in order to evaluate the possible bound state, we have also obtained the scattering lenghts. Our current results greatly improved previous {\it ab-initio} calculations showing a significantly better agreement between the theoretical results and experimental results, particularly at low angles for the differential cross sections.