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 × 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 ≥ 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.