  We study thermal leptogenesis in realistic supersymmetric flipped
$SU(5)\times U(1)$ unification. As up-type quarks and neutrinos are arranged in
the same multiplets, they exhibit strong correlations, and it is commonly
believed that the masses of right-handed (RH) neutrinos are too hierarchical to
fit the low-energy neutrino data. This pattern generally predicts a lightest RH
neutrino too light to yield successful leptogenesis, with any lepton-antilepton
asymmetry generated from heavier neutrinos being washed out unless special
flavour structures are assumed. We propose a different scenario in which the
lightest two RH neutrinos $N_1$ and $N_2$ have nearby masses of order $10^9$
GeV, with thermal leptogenesis arising non-resonantly from both $N_1$ and
$N_2$. We show that this pattern is consistent with all data on fermion masses
and mixing and predicts the lightest physical left-handed neutrino mass to be
smaller than about $10^{-7}$ eV. The Dirac phase, which does not take the
maximal CP-violating value, plays an important role in leptogenesis.
