  We develop a manifestly gauge-covariant expansion and projection using the
eigen-mode of the QCD Dirac operator. Applying this method to the Wilson loop
and the Polyakov loop, we perform a direct analysis of the correlation between
confinement and chiral symmetry breaking in SU(3) lattice QCD calculation on
6^4 at beta=5.6 at the quenched level. Notably, the Wilson loop is found to
obey the area law, and the slope parameter corresponding to the string tension
or the confinement force is almost unchanged, even after removing the low-lying
Dirac modes, which are responsible to chiral symmetry breaking. We find also
that the Polyakov loop remains to be almost zero even without the low-lying
Dirac modes, which indicates the Z_3-unbroken confinement phase. These results
indicate that one-to-one correspondence does not hold between confinement and
chiral symmetry breaking in QCD.
