  We consider the energy levels of a hydrogen-like atom in the framework of
$\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb
field. It is shown that on the noncommutative (NC) space the degeneracy of the
levels $2S_{1/2}, 2P_{1/2}$ and $ 2P_{3/2}$ is lifted completely, such that new
transition channels are allowed.
