  We present a theoretical study of the ionization dynamics of a hydrogen atom
exposed to attosecond laser pulses in the extreme ultra violet region at very
high intensities. The pulses are such that the electron is expected to reach
relativistic velocities, thus necessitating a fully relativistic treatment. We
solve the time dependent Dirac equation and compare its predictions with those
of the corresponding non-relativistic Schr{\"o}dinger equation. We find that as
the electron is expected to reach about 20% of the speed of light, relativistic
corrections introduces a finite yet small decrease in the probability of
ionizing the atom.
