  Positronium is an ideal system for the research of QED in the bound state.
The hyperfine splitting of positronium (Ps-HFS: about 203 GHz) is a good tool
to test QED and also sensitive to new physics beyond the Standard Model.
Previous experimental results show 3.9\,$\sigma$ (15 ppm) discrepancy from the
QED $\mathrm{O}\left(\alpha ^3 \ln{1/\alpha}\right)$ prediction. We point out
probable common systematic errors in all previous experiments. I measure the
Ps-HFS in two different ways. (1) A prototype run without RF system is
described first. (2) I explain a new direct Ps-HFS measurement without static
magnetic field. The present status of the optimization studies and current
design of the experiment are described. We are now taking data of a test
experiment for the observation of the direct transition.
