  Under amplitude damping channel, the dependence of the entanglement on the
initial states $|\Theta>_{1}$ and $|\Theta>_{2}$, which reduce to four
orthogonal Bell states if we take the parameter of states $\alpha=\pm
1/\sqrt{2}$ are investigated. We find that the entanglements for different
initial states will decay along different curves even with the same
acceleration 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 the
entanglement for $|\Theta>_{1}$ is larger than that for $|\Theta>_{2}$. There
exist two groups of Bell state here we can't distinguish only by concurrence.
