We analyze an extension of the Standard Model with an additional $SU\left(2\right)$ hypercolor gauge group keeping the Higgs boson as a fundamental field. Vectorlike interactions of new hyperquarks with the intermediate vector bosons are explicitly constructed. We also consider pseudo-Nambu–Goldstone bosons caused by the symmetry breaking $SU\left(4\right)\to Sp\left(4\right)$. A specific global symmetry of the model with zero hypercharge of the hyperquark doublets ensures the stability of a neutral pseudoscalar field. Some possible manifestations of the lightest states at colliders are also examined.