  The ground state hyperfine splitting of positronium $\Delta_{\mathrm{HFS}}$
is sensitive to high order corrections of quantum electrodynamics (QED) in
bound state. The theoretical prediction and the averaged experimental value for
$\Delta_{\mathrm{HFS}}$ has a discrepancy of 15 ppm, which is equivalent to 3.9
standard deviations (s.d.). A new precision measurement which reduces the
systematic uncertainty from the positronium thermalization effect was
performed, in which the non-thermalization effect was measured to be as large
as $10 \pm 2\,{\mathrm{ppm}}$ in a timing window we used. When this effect is
taken into account, our new result becomes $\Delta_{\mathrm{HFS}} = 203.394\,2
\pm 0.001\,6 ({\mathrm{stat., 8.0\,ppm}}) \pm 0.001\,3 ({\mathrm{sys.,
6.4\,ppm}})$\,GHz, which favors the QED prediction within 1.2 s.d. and
disfavors the previous experimental average by 2.6 s.d.
