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We obtain the exact values of the systoles of these hyperbolic surfaces of genus g with cyclic symmetry of the maximum order and the next maximum order.Precisely,for the genus g hyperbolic surface with order 4g+2 cyclic symmetry,the systole is 2arccosh(1+cos π/2g+1+cos 2π/2g+1)when g≥7,and for the genus g hyperbolic surface with order 4g cyclic symmetry,the systole is 2arccosh(1+2cosπ/2g)when g≥4.