  We propose a generic framework in which the Higgs and the unparticle are both
composite. The underlying theories are four dimensional, asymptotically free,
nonsupersymmetric gauge theories with fermionic matter. We sketch a possible
uni- fication of these two sectors at a much higher scale resembling extended
technicolor models. By construction our extensions are natural, meaning that
there is no hierar- chy problem. The coupling of the unparticle sector to the
composite Higgs emerges as a four-fermion operator. The bilinear unparticle
operator near the electroweak scale has scaling dimension in the range 1 < dU <
3. We investigate, in various ways, the breaking of scale invariance induced by
the electroweak scale resulting in an unparticle condensate. The latter acts as
a natural infrared cut off or hadronic scale. We give the low-energy effective
theory valid near the electroweak scale. The unparticle Higgs mixing is found
to be suppressed within our framework.
