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Under amplitude damping channel, the dependence of the entanglement on theinitial states $|\Theta>_{1}$ and $|\Theta>_{2}$, which reduce to fourorthogonal Bell states if we take the parameter of states $\alpha=\pm1/\sqrt{2}$ are investigated. We find that the entanglements for differentinitial states will decay along different curves even with the sameacceleration and parameter of the states. We note that, in an inertial frame,the sudden death of the entanglement for $|\Theta>_{1}$ will occur if$\alpha>1/\sqrt{2}$, while it will not take place for $|\Theta>_{2}$ for any$\alpha$. We also show that the possible range of the sudden death of theentanglement for $|\Theta>_{1}$ is larger than that for $|\Theta>_{2}$. Thereexist two groups of Bell state here we can't distinguish only by concurrence.

Dependence of entanglement on initial states under amplitude damping channel in non-inertial frames