  The assumption that space-time is a noncommutative space formed as a product
of a continuous four dimensional manifold times a finite space predicts, almost
uniquely, the Standard Model with all its fermions, gauge fields, Higgs field
and their representations. A strong restriction on the noncommutative space
results from the first order condition which came from the requirement that the
Dirac operator is a differential operator of order one. Without this
restriction, invariance under inner automorphisms requires the inner
fluctuations of the Dirac operator to contain a quadratic piece expressed in
terms of the linear part. We apply the classification of product noncommutative
spaces without the first order condition and show that this leads immediately
to a Pati-Salam SU(2)_{R}x SU(2)_{L}x SU(4) type model which unifies leptons
and quarks in four colors. Besides the gauge fields, there are 16 fermions in
the (2,1,4)+(1,2,4) representation, fundamental Higgs fields in the (2,2,1),
(2,1,4) and (1,1,1+15) representations. Depending on the precise form of the
order one condition or not there are additional Higgs fields which are either
composite depending on the fundamental Higgs fields listed above, or are
fundamental themselves. These additional Higgs fields break spontaneously the
Pati-Salam symmetries at high energies to those of the Standard Model.
