  In scenarios of strongly coupled electroweak symmetry breaking, heavy
composite particles of different spin and parity may arise and cause observable
effects on signals that appear at loop levels. The recently observed process of
Higgs to $\gamma \gamma$ at the LHC is one of such signals. We study the new
constraints that are imposed on composite models from $H\to \gamma\gamma$,
together with the existing constraints from the high precision electroweak
tests. We use an effective chiral Lagrangian to describe the effective theory
that contains the Standard Model spectrum and the extra composites below the
electroweak scale. Considering the effective theory cutoff at $\Lambda = 4\pi v
\sim 3 $ TeV, consistency with the $T$ and $S$ parameters and the newly
observed $H\to \gamma\gamma$ can be found for a rather restricted range of
masses of vector and axial-vector composites from $1.5$ TeV to $1.7$ TeV and
$1.8$ TeV to $1.9$ TeV, respectively, and only provided a non-standard kinetic
mixing between the $W^{3}$ and $B^{0}$ fields is included.
