Under amplitude damping channel, the dependence of the entanglement on the initial states and , which reduce to four orthogonal Bell states if we take the parameter of statesare 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 will occur if, while it will not take place for for any α. We also show that the possible range of the sudden death of the entanglement for is larger than that forThere exist two groups of Bell state here we can't distinguish only by concurrence.