  Positronium is an ideal system for the research of the quantum
electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of
positronium, $\Delta_{\mathrm{HFS}}$, gives a good test of the bound state
calculations and probes new physics beyond the Standard Model. A new method of
QED calculations has revealed the discrepancy by 15\,ppm (3.9$\sigma$) of
$\Delta_{\mathrm{HFS}}$ between the QED prediction and the experimental
average. There would be possibility of new physics or common systematic
uncertainties in the previous all experiments. We describe a new experiment to
reduce possible systematic uncertainties and will provide an independent check
of the discrepancy. We are now taking data and the current result of
$\Delta_{\mathrm{HFS}} = 203.395\,1 \pm 0.002\,4 (\mathrm{stat.},
12\,\mathrm{ppm}) \pm 0.001\,9 (\mathrm{sys.}, 9.5\,\mathrm{ppm})\,\mathrm{GHz}
$ has been obtained so far. A measurement with a precision of $O$(ppm) is
expected within a year.
