  A field model for a quark and an antiquark binding is described. Quarks
interact via a gauge unparticle ("ungluons"). The model is formulated in terms
of Lagrangian which features the source field $S(x)$ which becomes a local
pseudo-Goldstone field of conformal symmetry - the pseudodilaton mode and from
which the gauge non-primary unparticle field is derived by $B_{\mu}(x)
\sim\partial_{\mu} S(x)$. Because the conformal sector is strongly coupled, the
mode $S(x)$ may be one of new states accessible at high energies. We have
carried out an analysis of the important quantity that enters in the "ungluon"
exchange pattern - the "ungluon" propagator.
