  We consider an electron moving under a constant magnetic field (in the
z-direction) and a \textit{linear} electric field parallel to the magnetic
field above the z=0 plane and anti-parallel below the plane. Two frequencies
characterize the system: the cyclotron frequency $\omega_c$ corresponding to
motion along the x-y plane and associated with the usual Landau levels, and a
second frequency $\omega_z$ corresponding to motion along the z-direction. In
previous work, the non-relativistic energies of this system were obtained, and
it was shown that an extra degeneracy (beyond the Landau degeneracy) occurs
when the ratio $\text{w}=\omega_c/\omega_z$ is rational. In this paper, we use
Dirac's equation to obtain compact formulas for the first and second order
relativistic corrections to this system via perturbation theory. The formulas
are expressed in terms of the two frequencies $\omega_c$ and $\omega_z$, and
two quantum numbers, $n$ and $n_z$, both of which are non-negative integers.
The first order correction is negative and lowers the original energies. We
plot the energy (zeroth plus first order) versus the ratio $\text{w}$ and there
are degeneracies at all points where lines intersect. However, the degeneracy
does not occur at the same $\text{w}$ as before. To illustrate this, we show
how the first order correction splits the energy levels for the case
$\omega_c=\omega_z$.
