  We investigate two-party quantum teleportation through noisy channels for
multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and find which state loses
less quantum information in the process. The dynamics of states is described by
the master equation with the noisy channels that lead to the quantum channels
to be mixed states. We analytically solve the Lindblad equation for $n$-qubit
GHZ states $n\in\{4,5,6\}$ where Lindblad operators correspond to the Pauli
matrices and describe the decoherence of states. Using the average fidelity we
show that 3GHZ state is more robust than $n$GHZ state under most noisy
channels. However, $n$GHZ state preserves same quantum information with respect
to EPR and 3GHZ states where the noise is in $x$ direction in which the
fidelity remains unchanged. We explicitly show that Jung ${\it et\, al.}$
conjecture [Phys. Rev. A ${\bf 78}$, 012312 (2008)], namely, "average fidelity
with same-axis noisy channels are in general larger than average fidelity with
different-axis noisy channels" is not valid for 3GHZ and 4GHZ states.
