  We determine the strange quark mass ($m_s$) and quark mixing element $\vert
V_{us}\vert $, and their joint determination from the Cabibbo suppressed
hadronic $\tau$ decays in various perturbative schemes. Compared to the
previous analysis based on the optimal renormalization or the renormalization
group summed perturbation theory (RGSPT) scheme, we have improved this analysis
by replacing the theoretical longitudinal contributions with phenomenological
parametrization, and the RGSPT coefficients are used for the dimension-4 Adler
functions. The improved analysis results in the extraction of
$m_s(2\,\mathrm{GeV})=98\pm19\,\mathrm{MeV}$ and $\vert
V_{us}\vert=0.2191\pm0.0043$ from the RGSPT scheme.
