  We introduce a natural origin of the Peccei-Quinn (PQ) symmetry with a
sufficiently good precision. In the standard model, the baryon number symmetry
U(1)_B arises accidentally due to the SU(3)_C color gauge symmetry, and it
protects the proton from a decay at a sufficient level. Likewise, if there is
an SU(N) gauge symmetry in the hidden sector, an accidental hidden baryon
number symmetry U(1)_{B_H} can appear. The hidden baryon number is solely
obtained by the structure of the SU(N) group. In particular, the quality of the
U(1)_{B_H} can be arbitrarily good for an asymptotically-free theory with large
enough N. The U(1)_{B_H} can be identified as a PQ symmetry. Using our
findings, we build two types of novel composite axion models: a model where
only one SU(N) gauge symmetry is required to both guarantee the quality and
break the U(1)_{B_H}, and a model with SU(N)xSU(M) gauge symmetry where the
exotic quarks responsible to the axion-gluon coupling do not confine into
exotic hadrons through the dynamical breaking of the PQ symmetry, and have
masses of TeV scales.
