Starting from the multi‐local Klein‐Gordon equations with Lorentz‐scalar squared‐mass operator we give a covariant quark representation of the general composite mesons and baryons with definite Lorentz transformation property. The mass spectra satisfy the approximate symmetry under theU˜(4) transformation group, including the chiral transformation as a subgroup, concerning the spinor freedom of light constituent quarks, and this symmetry predicts the existence of new type of chiral mesons and baryons out of the conventional framework in non‐relativistic quark model: For example, for lightqq¯systems, the scalar &sgr;‐ and axial‐vectora1‐nonets, and for heavy‐lightQq¯andqQ¯systems the scalar and axial‐vector mesons are predicted to exist as relativisticS‐wave states besides the ordinaryP‐wave state mesons. The existence of two “exotic” 1−+meson nonets is predicted as the relativisticP‐wave states inqq¯systems. For light quark baryons the extra56with positive parity and the extra70with negative parity of the staticSU(6) are predicted to exist as the ground state chiral particles. © 2002 American Institute of Physics