We have already proposed a method for analyzing the nonlinear vibration response properties of rubber in relation to frequency and amplitude of displacement (Ref. (3)). That method determined the predominant frequency of rubber itself by using the FFT (Fast Fourier Transform). In this paper, we describe a new method for analyzing nonlinear vibration response. This method determines the predominant frequency of relative displacement of rubber itself by using a period on each one of the hysteresis loops. We were able to verify the appropriateness and accuracy of this method by directly comparing the analytical results with the experimental results for the dynamic response of a system. This new method compares favorably with the method of Ref. (3) in terms of the accuracy of calculation. We consider that our method may be applicable to a multiple-degree-of-freedom system.