  Using the eigen-mode of the QCD Dirac operator $\Slash D=\gamma^\mu D^\mu$,
we develop a manifestly gauge-covariant expansion and projection of the QCD
operators such as the Wilson loop and the Polyakov loop. With this method, we
perform a direct analysis of the correlation between confinement and chiral
symmetry breaking in lattice QCD Monte Carlo calculations. Even after removing
the low-lying Dirac modes, which are responsible to chiral symmetry breaking,
we find that the Wilson loop obeys the area law, and the string tension or the
confinement force is almost unchanged. 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.
