  We determine the strong coupling constant \alpha_s from the \tau hadroni
width using a renormalization group summed (RGS) expansion of the QCD Adler
function. The main theoretical uncertainty in the extraction of \alpha_s is due
to the manner in which renormalization group invariance is implemented, and the
as yet uncalculated higher order terms in the QCD perturbative series. We show
that new expansion exhibits good renormalization group improvement and the
behaviour of the series is similar to that of the standard CIPT expansion. The
value of the strong coupling in {\bar{\rm MS}} scheme obtained with the RGS
expansion is \alpha_s(M_\tau^2)= 0.338 \pm 0.010. The convergence properties of
the new expansion can be improved by Borel transformation and analytic
continuation in the Borel plane. This is discussed elsewhere in these
proceedings.
