  We compute to next-to-leading order in QCD the tensor unparticle contribution
to the diphoton production at the LHC, wherein the unparticle sector is a
consequence of (a) scale invariance but not full conformal invariance and (b)
conformal invariance. We use the semi-analytical two cutoff phase space slicing
method to handle the ${\cal O}(\alpha_s)$ corrections to the $p p \to \gamma
\gamma X$ and show that our results are insensitive to the soft and collinear
cutoffs. In order to avoid the contribution of the photons due to
fragmentation, we employ the smooth cone isolation criterion. Significance of
the QCD corrections to the diphoton events including unparticles is
highlighted.
