  We show the first lattice QCD results on the axial charge $g_A^{N^*N^*}$ of
$N^*(1535)$ and $N^*(1650)$. The measurements are performed with two flavors of
dynamical quarks employing the renormalization-group improved gauge action at
$\beta$=1.95 and the mean-field improved clover quark action with the hopping
parameters, $\kappa$=0.1375, 0.1390 and 0.1400. In order to properly separate
signals of $N^*(1535)$ and $N^*(1650)$, we construct 2$\times$2 correlation
matrices and diagonalize them. Wraparound contributions in the correlator,
which can be another source of signal contaminations, are eliminated by
imposing the Dirichlet boundary condition in the temporal direction. We find
that the axial charge of $N^*(1535)$ takes small values as $g_A^{N^*N^*}\sim
{\mathcal O}(0.1)$, whereas that of $N^*(1650)$ is about 0.5, which is found
independent of quark masses and consistent with the predictions by the naive
nonrelativistic quark model.
