  Motivated by the recent work on the calculation of the $\pi NN$ coupling
constant using QCD sum rule beyond the chiral limit, we construct the
corresponding sum rules for the couplings, $\eta NN$, $\pi \Xi\Xi$, $\eta
\Xi\Xi$, $\pi \Sigma \Sigma$ and $\eta \Sigma \Sigma$. In constructing the
$\eta$-baryon sum rules, we use the second moment of the $\eta$ wave function,
which we obtain from the pion wave function after SU(3) rotation. In the SU(3)
symmetric limit, we can identify the term responsible for the $F/D$ ratio in
the OPE, which after the sum rule analysis gives $F/D\sim 0.2$, a factor of 3
smaller than from other studies. We also present a qualitative analysis
including the
  SU(3) breaking terms.
