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PROBLEM TO BE SOLVED : To provide a preparation method of a catalyst with high activity.SOLUTION : There is provided a catalyst preparation method including a process of reacting only a rare earth element compound (A) of the formula (I) : M-(AQ1)(AQ2)(AQ3), where M is a lanthanoid element, scandium or yttrium, AQ1, AQ2 and AQ3 are functional groups containing one or more of nitrogen, oxygen and sulfur, or substituted or unsubstituted cyclopentadienyl groups, indenyl groups or fluorenyl groups and has an M-N bond, an M-O bond or an M-S bond, an aluminoxane compound (B) and an organic metal compound (C) of the formula (II) : YR1aR2bR3c, where Y is a metal element of the Group 1, the Group 2, the Group 12 or the Group 13 in the periodic table, R1 and R2 are hydrocarbon group having 1 to 10 carbon atoms or hydrogen atoms, R3 is a hydrocarbon group having 1 to 10 carbon atoms, a is 1 and b and c are 0; a and b are 1 and c is 0; or a, b and c are 1.SELECTED DRAWING : NoneCOPYRIGHT : (C)2017, JPO&INPIT