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We study the effect of Kerr medium on the intrinsic decoherence of a system which consists of two two-Jevel atoms and a optical cavity. The entanglement of the system is calculated by making use of concurrence. Our results show that the intrinsic decoherence is very sensitive to the nonlinear coupling constant of Kerr medium. Both the oscillation period and the amplitude of the concurrence increase with the increasing nonlinear coupling constant.