  We discuss a supersymmetric grand unified model which has gauge group SU(5)
$\times$ SU(5) $\times$ SU(5), with matter fields transforming asymmetrically
under different gauge SU(5) groups. We observe that the gauge structure of the
model leads to approximate texture zero structures in fermion mass matrices and
a natural hierarchy in the Yukawa couplings. The proton lifetime is estimated
to be larger than $10^{34}$ years in this model. As in more conventional
supersymmetric GUT models with product gauge groups, this model possesses no
tensor fields with rank higher than 2, so that it might arise from a level 1
string construction.
