  We study the heterotic asymmetric orbifold model in which supersymmetry is
broken by the stringy Schark-Schwarz mechanism. This model is a natural
non-supersymmetric extension of CHL strings and can also be interpreted as the
interpolating model between the $E_{8}\times E'_{8}$ theory and the
non-supersymmetric $E_{8}$ theory. The enhancement of gauge groups, of which
the rank is reduced to $8+d$, is explored. In particular, the enhancement to
non-simply-laced groups is possible with $d\geq 2$, as well as in the CHL
model. We also give the conditions that the massless matter spectrum must
satisfy. Moreover, the one-loop cosmological constant is evaluated in the
regime where supersymmetry is asymptotically restored, and we show that the
exponential suppression can occur unless $d=1$.
