  Composite Higgs models provide an attractive solution to the hierarchy
problem. However, many realistic models suffer from tuning problems in the
Higgs potential. There are often large contributions from the UV dynamics of
the composite resonances to the Higgs potential, and tuning between the
quadratic term and the quartic term is required to separate the electroweak
breaking scale and the compositeness scale. We consider a composite Higgs model
based on the $SU(6)/Sp(6)$ coset, where an enhanced symmetry on the fermion
resonances can minimize the Higgs quadratic term. Moreover, a Higgs quartic
term from the collective symmetry breaking of the little Higgs mechanism can be
realized by the partial compositeness couplings between elementary Standard
Model fermions and the composite operators, without introducing new elementary
fields beyond the Standard Model and the composite sector. The model contains
two Higgs doublets, as well as several additional pseudo-Nambu-Goldstone
bosons. To avoid tuning, the extra Higgs bosons are expected to be relatively
light and may be probed in the future LHC runs. The deviations of the Higgs
couplings and the weak gauge boson couplings also provide important tests as
they are expected to be close to the current limits in this model.
