Abstract: The coherency coefficients in the multi-support response spectrum analysis are modified from two aspects:the characteristics of the frequency response function and the integral.First of all,H_i(ω)H_j(ω)^* is separated into real and image components.Then,according to the integral characteristic,the integration layers of the coherency coefficients ρ_ijkl are reduced from i×j×k×l(i、j are the numbers of the vibration mode;k、l are the numbers of the support)to 5×j×k×l,which shortens the calculated time but it is still accurate.The simplification makes the multi-support response spectrum analysis easier to conduct.