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 the U{top}～ (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 light qq{top}- systems, the scalar σ- and axial-vector a{sub}1-nonets, and for heavy-light Qq{top}- and qQ{top}- systems the scalar and axial-vector mesons are predicted to exist as relativistic S-wave states besides the ordinary P-wave state mesons. The existence of two "exotic" 1{sup}(-+) meson nonets is predicted as the relativistic P-wave states in qq{top}- systems. For light quark baryons the extra 56 with positive parity and the extra 70 with negative parity of the static SU(6) are predicted to exist as the ground state chiral particles.
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