Symmetry Breaking in $[SU(6){]}^3\times Z_3$

We analize the different ways for the spontaneous breaking of the gauge symmetry, for the $[SU(6){]}^3\otimes Z_3$ family unification model. In particular we study the consequences of a previous selection for the vacuum expectation values of the Higgs fields, showing that such set predicts unwanted flavor changing neutral currents at the $m_Z=91GeVs$ mass scale. A new set of vacuum expectation values which solves this problem is proposed.