We discuss a composite two Higgs doublet model based on a symmetry breaking SO(6) × U (1) x → SO(4) ×SO(2) × U (1)x at a scale f, and explain how the effective kinetic Lagrangian of the model is obtained. The coupling of the Higgs boson as a pseudo Nambu-Goldstone boson to the standard model fields can deviate from that of the standard model Higgs boson due to the non-linear feature. These deviations cause to unitarity violation at high energies because the cancellation of the quadratic energy terms does not happen. We calculate the S-wave amplitude for all the possible two body to two body elastic scalar boson scatterings at the energy \sqrt{s} which involve the longitudinal component of weak gauge boson states as the corresponding Nambu-Goldstone boson states via the Equivalence Theorem Approximation.

We will examine the constrains on parameter space from perturbative unitarity with a fixed energy scale in the composite two Higgs doublet model. By requiring all the eigenvalues of the S-wave matrix to be smaller than a certain value, we obtain constraints on the parameter space such as s, ξ and masses of extra Higgs bosons. We show that stronger upper bounds on the masses of the CP-even and CP-odd Higgs bosons are obtained under the constraints from the unitarity and vacuum stability conditions.