  The large top Yukawa coupling results in the top quark contributing
significantly to the quantum correction of the Higgs mass term. Traditionally,
this effect is canceled by the presence of top partners in symmetry-based
models. However, the absence of light top partners poses a challenge to the
Naturalness of these models. In this paper, we study a model based on composite
Higgs with the top Yukawa coupling originating from dimension-six four-fermion
operators. The low cutoff scale of the top quark loop required by the
Naturalness principle can be realized with a light gauge boson $E_\mu$ which
connects the hyperfermions and top quarks. A scalar-less dynamical model with
weakly coupled extended $SU(4)_{EC}$ gauge group is presented. The model
features an $E_\mu$ boson and a $Z'_E$ boson both at the sub-TeV scale, which
lead to a rich phenomenology, especially in the top physics.
