  Unparticles charged under a gauge group can contribute to the running of the
gauge coupling. We show that a scalar unparticle of scaling dimension d
contributes to the \beta function a term that is (2-d) times that from a scalar
particle in the same representation. This result has important implications on
asymptotic freedom. An unparticle with d>2, in contrast to its matter
counterpart, can speed up the approach to asymptotic freedom for a non-Abelian
gauge theory and has the tendency to make an Abelian theory also asymptotically
free. For not spoiling the excellent agreement of the standard model (SM) with
precision tests, the infrared cut-off, m, of such an unparticle would be high
but might still be reachable at colliders such as LHC and ILC. Furthermore, if
the unparticle scale \Lambda_\calU is high enough, unparticles could
significantly modify the unification pattern of the SM gauge couplings. For
instance, with 3 scalar unparticles of d\sim 2.5 in the adjoint representation
of the strong gauge group but neutral under the electroweak one, the three
gauge couplings would unify at a scale of \sim 8\times 10^{12} {\rm GeV}, which
is several orders of magnitude below the supersymmetric unification scale.
