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Positronium (Ps) is a bound state of an electron and a positron, which annihilates into photons. It is a suitable place to study quantum electrodynamics (QED) since strong and weak interactions are negligibly small in the annihilation processes. Our experimental group has been measuring rare annihilation processes from Ps using a multi-{gamma}-ray spectrometer called UNI which consists of 32 NaI(Tl)(3``{phi} x 4``) scintillation counters. We had detected the 4{gamma} and 5{gamma} annihilation processes firstly. In the experiment, 256 events of 4{gamma} annihilation process has been accumulated until today. Using the momentum chirality method, which I propose firstly, we have studied the parity invariance in the higher order QED region at 1 MeV/c order momentum transfer. The results of this study shows the value|a{sub symmetry}|{sub upper} {sub limit} which we defined to estimate one kind of parity invariance is represented as 1.0 x 10{sup -1} at 90% confidence level. We conclude that no evidence of the parity violation has been observed in the collected e{sup +}e{sup -} {yields} 4{gamma} 256 events. To improve the upper limit of parity invariance, much more events must be collected. We propose a new multi-{gamma}-ray spectrometer, Super UNI which consists of 92 GSO(Ce) (2``{phi} x 2``) scintillation counters, which can collect the e{sup +}e{sup -} {yields} 4{gamma} 10,000 events in the same period that previous experiment. (author)