  We have studied entanglement between two Dirac modes respectively observed by
two independently accelerated observers. Due to Unruh effect, the entanglement
degrades, but residual nonzero entanglement remains even when the accelerations
of both observers are infinite. We have also investigated quantum teleportation
using entangled Dirac modes, and calculated the fidelities in various cases. In
general, the fidelity depends on the single-qubit state $\gamma|0\rangle
+\delta|1\rangle$ to be teleported, as well as which Bell state to use. In the
limit that both accelerations are infinite, the average fidelity in using
$|\phi^\pm\rangle\equiv\frac{1}{2}(|00\rangle\pm |11\rangle) $ is
$\frac{3}{4}$, while that in using $|\psi^\pm\rangle\equiv \frac{1}{2}
(|01\rangle\pm |10\rangle) $ is $\frac{1}{2} + |\gamma|^2 |\delta|^2$.
