  We show that Lorentz symmetry is generally absent for noncommutative
(abelian) gauge theories and obtain a compact formula for the divergence of the
Noether currents that allows a throughout study of this instance of symmetry
violation. We use that formula to explain why the results of "Noncommutative
gauge theories and Lorentz symmetry", Phys. Rev. D {\bf 70}, 125004 (2004) by
R.Banerjee, B.Chakraborty and K.Kumar, interpreted there as new criteria for
Lorentz {\it invariance}, are in fact just a particular case of the general
expression for Lorentz {\it violation} obtained here. Finally, it is suggested
that the divergence-formula should hold in a vast class of cases, such as, for
instance, the Standard Model Extension.
