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

New non-supersymmetric heterotic string theory with reduced rank and exponential suppression of the cosmological constant