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 (S x k{1})(S x k{1}x k{2}), where S is the positronium spin and k{1}, k{2} are the directions of the positronium decay photons. To a sensitivity of 2.2x10{-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.