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%.
