In a (0,1) supersymmetric (SUSY) six-dimensional gauge theory, a gaugefermion gives rise to box anomalies. These anomalies are completely canceled byassuming a vector multiplet of (1,1) SUSY. With a T^2/Z_3 orbifoldcompactification of the extra two dimensional space, the theory provides threechiral multiplets and three equivalent fixed points. We regard them as theorigin of the three families of quarks and leptons. Quasi anarchy structure inthe SU(5)-5^* representation sector and hence the bimaximal mixing in theneutrino oscillation are explained quite naturally in this framework. We alsodiscuss a family symmetry as a remnant of the higher-dimensional R symmetry.