  The effect of the Gauss--Bonnet term on the SU(2) non--Abelian regular
stringy sphaleron solutions is studied within the non--perturbative treatment.
It is found that the existence of regular solutions depends crucially on the
value of the numerical factor $\beta$ in front of the Gauss--Bonnet term in the
four--dimensional effective action. Numerical solutions are constructed in the
N=1, 2, 3 cases for different $\beta$ below certain critical values $\beta_N$
which decrease with growing N (N being the number of nodes of the Yang--Mills
function). It is proved that for any static spherically symmetric
asymptotically flat regular solution the ADM mass is exactly equal to the
dilaton charge. No solutions were found for $\beta$ above critical values, in
particular, for $\beta=1$.
