  We present a variation of the NAHE-basis for free fermionic heterotic string
models. By rotating some of the boundary conditions of the NAHE
periodic/anti-periodic fermions {y^m, \bar{y}^m, w^m, \bar{w}^m,}, for m = 1 to
6, associated with the six compact dimensions of a bosonic lattice/orbifold
model, we show an additional method for enhancing the standard NAHE gauge group
of SO(10) back to E6. This rotation transforms (SO(10) {\otimes} SO(6)^3)_obs
{\otimes} (E_8)_hid into (E_6 {\otimes} U(1)^5)_obs {\otimes} SO(22)_hid. When
SO(10) is enhanced to E_6 in this manner, the i^{th} MSSM matter generation in
the SO(10) 16_i rep, originating in the twisted basis vector b_i, recombines
with both its associated untwisted MSSM Higgs in a 10_i rep and an untwisted
non-Abelian singlet {\phi}_i, to form a 27_i rep of E_6. Beginning instead with
the E6 model, the inverse transformation of the fermion boundary conditions
corresponds to partial GUT breaking via boundary rotation. Correspondence
between free fermionic models with Z_2 {\otimes} Z_2 twist (especially of the
NAHE class) and orbifold models with a similar twist has received further
attention recently. Our NAHE variation also involves a Z_2 {\otimes} Z_2 twist
and offers additional understanding regarding the free fermion/orbifold
correspondence. Further, models based on this NAHE variation offer some
different phenomenological features compared to NAHE-based models. In
particular, the more compact Z2 {\otimes} Z2 twist of the NAHE variation offers
a range of mirror models not possible from NAHE-based models. Examples of such
models are presented.
