Abstract: With the help of Zerilli variable，the linearised Einstein equation can be reduced to a simple second order wave equation，from which we solve the quasi-normal frequency routinely. However，if we try to calculate the perturbed metric them selves，we need to do one extra time integration and many spatial differentials on the power serial form master variables. This forms heavy burden for the second order perturbation calculation. This paper takes the perturbation metric components themselves (either one of the three) as master variables and derives out their differential equations directly，which are spatially differentiated three times and temporarily differentiated twice. We solve this equation by the usual power serial method and get quasi-normal frequencies coincident with those solved out from Zerilli equation，thus we establish an equivalences between the two methods and making much advantageous preparation for higher order perturbations calculation.

Key words:  spherical symmetric black holes, even parity perturbation, quasi-normal modes