  We apply the method of the QCD sum rule, in which positive- and
negative-parity baryons couple with each other, to the flavor-octet hyperons
and investigate the parity splittings. We also reexamine the nucleon in the
method, which was studied in our previous paper, by carefully choosing the
Borel weight. Both in the nucleon and hyperon channels the obtained sum rules
turn out to have a very good Borel stability and also have a Borel window, an
energy region in which the OPE converges and the pole contribution dominates
over the continuum contribution. The predicted masses of the positive- and
negative-parity baryons reproduce the experimental ones fairly well in the
$\Lambda$ and $\Sigma$ channels, if we assign the $\Lambda(1670)$ and the
$\Sigma(1620)$ to the parity partners of the $\Lambda$ and the $\Sigma$,
respectively. This implies that the $\Lambda(1405)$ is not the party partner of
the $\Lambda$ and may be a flavor-singlet or exotic state. In the $\Xi$
channel, the sum rule predicts the mass of the negative-parity state to be
about 1.8 GeV, which leads to two possibilities; one is that the observed state
with the closest mass, $\Xi(1690)$, is the parity partner and the other is that
the parity partner is not yet found but exists around 1.8 GeV.
