The second solar spectrum (spectrum of the linear polarization observed near the solar limb in a quiet region) of Na I D1 has always been found antisymmetrical when observed with THEMIS tep{b12 TB01,b12 BM02}. The same holds also for atlas of tet{b12 Ga00}. On the contrary, tet{b12 SK97} and tet{b12 St00} observed a differently shaped profile, showing a central peak. We investigated in depth our treatment of THEMIS data, in particular looking for possible beam misalignments, by observing other unpolarized lines, but we have failed to put in evidence any misalignment. We discuss these complementary observations. In addition, we present a structure in the V/I profile of Na I D1 and D2, which we have repeatedly observed, and which we suggest be due to the Kemp effect (the alignement-to-orientation transfer that occurs in the transition from the Zeeman effect to the Paschen-Back effect).