  CP-violation in the quark sector has been well established over the last
decade, but has not been observed in the lepton sector. We search for
CP-violating decay processes in positronium, using the angular correlation of
(\vec{S}\cdot\vec{k_{1}})(\vec{S}\cdot\vec{k_{1}}\times\vec{k_{2}}), where
\vec{S} is the the positronium spin and \vec{k_{1}}, \vec{k_{2}} are the
directions of the positronium decay photons. To a sensitivity of
2.2\times10^{-3}, no CP-violation has been found, which is at the level of the
CP-violation amplitude in the K meson. A 90% confidence interval of the
CP-violation parameter (C_{CP}) was determined to be -0.0023 < C_{CP} < 0.0049.
This result is a factor 7 more strict than that of the previous experiment.
