  The entanglement between two modes of the free scalar and Dirac fields as
seen by two relatively accelerated observers has been investigated. It is found
that the same initial entanglement for an initial state parameter $\alpha$ and
its "normalized partner" $\sqrt{1-\alpha^{2}}$ will be degraded by the Unruh
effect along two different trajectories except for the maximally entangled
state, which just shows the inequivalence of the quantization for a free field
in the Minkowski and Rindler coordinates. In the infinite acceleration limit
the state doesn't have the distillable entanglement for any $\alpha$ for the
scalar field but always remains entangled to a degree which is dependent of
$\alpha$ for the Dirac field. It is also interesting to note that in this limit
the mutual information equals to just half of the initially mutual information,
which is independent of $\alpha$ and the type of field.
