  We study a non-supersymmetric SO(10) Grand Unification Theory with a very
high energy intermediate symmetry breaking scale in which not only gauge but
also Yukawa coupling unification are enforced via suitable threshold
corrections and matching conditions. For gauge unification, we focus on a few
symmetry breaking patterns with the intermediate gauge groups ${\rm SU(4)_C
\times SU(2)_L \times SU(2)_R}$ (Pati-Salam) and ${\rm SU(3)_C \times SU(2)_L
\times SU(2)_R\times U(1)_{B-L}}$ (minimal left-right symmetry) assuming an
additional global U(1) Peccei--Quinn symmetry, and having the Standard Model
supplemented by a second Higgs doublet field at the electroweak scale. We
derive the conditions as well as the approximate analytical solutions for the
unification of the gauge coupling constants at the two-loop level and discuss
the constraints from proton decay on the resulting high scale. Specializing to
the case of the Pati-Salam intermediate breaking pattern, we then impose also
the unification of the Yukawa couplings of third generation fermions at the
high scale, again at the two-loop level. In the considered context, Yukawa
unification implies a relation between the fermion couplings to the 10- and
126-dimensional scalar representations of the SO(10) group. We consider one
such possible relation which is obtainable in an ${\rm E_6}$ model where the
previous two scalar fields are part of a single multiplet. Taking into account
some phenomenological features such as the absence of flavor changing neutral
currents at tree-level, we derive constraints on the parameters of the low
energy model, in particular on the ratio of the two Higgs doublets vacuum
expectation values $\tan\beta$.
