  We present an investigation on the invariance properties of noncommutative
Yang-Mills theory in two dimensions under area preserving diffeomorphisms.
Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a
breaking of such an invariance, we confirm both on a fairly general ground and
by means of perturbative analytical and numerical calculations that indeed
invariance under area preserving diffeomorphisms is lost. However a remnant
survives, namely invariance under linear unimodular tranformations.
