Abstract: Motivated by SO(10), where the charge two-thirds and neutral Dirac Yukawa matrices are related, we propose a special form of the seesaw Majorana matrix. It not only can mitigate the severe hierarchy of the quark sector, but also contains a Gatto-Sartori-Tonin like relation, which predicts specific values for the light neutrino masses. Two different ways of obtaining that special Majorana matrix from the family symmetry $Z_7 rtimes Z_3$ will be presented. The first way requires a linear combination of two dimension-five family invariant operators, while in the second one a single dimension-six operator is needed.