As a result of "Ligand-Oriented Catalyst Design" research based on "Fundamentally Active Ligands", group 4 transition metal complexes having two phenoxy-imine chelate ligands, FI Catalysts, were found to exhibit very high ethylene polymerization activity using MAO as a cocatalyst. Among the complexes, zirconium complexes displayed the highest activity. The maximum activity exceeded 4 ton-PE/mmol-cat . h at 25 degreesC even under 1 atm of ethylene. This activity corresponds to a catalyst turnover frequency (TOF) value of 42,900/sec . aim, the TOF value being, in all likelihood, the largest for not only olefin polymerization but also any other catalytic reaction. Moreover, selecting the cocatalyst as well as changing the ligand structure revealed that the zirconium complexes produced polyethylene of low (Mv; 3x10(3)) to exceptionally high (Mv: 5x10(5)) molecular weight, while at the same time displaying high activity. Furthermore, Fl Catalysts can be easily synthesized, and possess wider range of catalyst design compared with the group 4 metallocene catalysts. These facts indicate that Fl Catalysts possess very high potential as a new generation of olefin polymerization catalysts.