  The strategy for assigning $Z_{4R}$ parity in the string compactification is
presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand
unification (GUT) model with three families is used to reduce the number of
representations compared to the number in the minimal supersymmetric standard
models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian
gauge group SU($N$), $N\ge 9$, for the hidden sector such that the number of
extra U(1) factors is small. A discrete subgroup of the gauge U(1)'s is defined
as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is
achieved by the vacuum expectation values of two index antisymmetric tensor
Higgs fields ${\bf 10}_{+1}$ and $\overline{\bf 10}_{-1}$ that led to our word
`anti-SU(5)'. In the illustrated example, the multiplicity 3 in one twisted
sector allows the permutation symmetry $S_3$ that leads us to select the third
family members and one MSSM pair of the Higgs quintets.
