  The first complete calculation of the quadratic quark mass correction to the
correlator of the two currents relevant for the strangeness-changing
semihadronic tau-decay rate is presented including its real part at the
four-loop level. This allows to perform the extraction of the strange quark
mass m_s from the decay width of the tau-lepton with full O(alpha_s^3)
accuracy. In agreement with previous estimates the newly computed alpha_s^3
term proves to be rather large. This justifies inclusion of the similarly
estimated alpha_s^4 term in phenomenological analysis. Combined with an updated
value of V_{us} and an ``'improved'' version of the renormalization group
improvement of the perturbative series this leads to an increase of the central
value of m_s by about 20 % and a partial reduction of the theoretical
uncertainty by about 50 %.
