  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 tilde U(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
qqbar systems, the scalar sigma- and axial-vector a_1-nonets, and for
heavy-light Qqbar and qQbar 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^-+ meson nonets is predicted as
the relativistic P-wave states in qqbar 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.
