  The one-tangle and {\pi}-tangle are used to quantify the entanglement of a
tripartite GHZ state in noninertial frames when the system interacts with a
noisy environment in the form of phase damping, phase flip and bit flip
channel. It is shown that the two-tangles behave as a closed system. The
one-tangle and {\pi}-tangle have different behaviors in the three channel. In
the case of phase damping channel, depending on the kind of coupling, the
sudden death of both one-tangle and {\pi}-tangle may or may not happen. Whereas
in the case of phase flip channel the sudden death cannot be avoided. The
effect of decoherence may be ignored in the limit of infinite acceleration when
the system interacts with a bit flip channel. Furthermore, a sudden rebirth of
the one-tangle and {\pi}-tangle occur in the case of phase flip channel that
may be delayed when collective coupling is switched on.
