  We extend the Minimum Supersymmetry Standard Model by a non-anomalous family
(NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are cancelled with no
additional exotics other than the three right-handed neutrinos. The FI D-terms
associated with the U(1)'_{NAF} symmetry lead to additional positive
contributions to slepton squared masses. In a RG invariant way, this thus
solves the tachyonic slepton mass problem in Anomaly Mediated Supersymmetry
Breaking. In addition, the U (1)'_{NAF} symmetry naturally gives rise to the
fermion mass hierarchy and mixing angles, and determines the mass spectrum of
the sparticles.
