  We define a noncommutative Lorentz symmetry for canonical noncommutative
spaces. The noncommutative vector fields and the derivatives transform under a
deformed Lorentz transformation. We show that the star product is invariant
under noncommutative Lorentz transformations. We then apply our idea to the
case of actions obtained by expanding the star product and the fields taken in
the enveloping algebra via the Seiberg-Witten maps and verify that these
actions are invariant under these new noncommutative Lorentz transformations.
We finally consider general coordinate transformations and show that the metric
is undeformed.
