  We give a pedagogical analysis on $K$ matrix models describing the $\pi N$
scattering amplitude, in $S_{11}$ channel at low energies. We show how the
correct use of analyticity in the $s$ channel and crossing symmetry in $t$ and
$u$ channels leads to a much improved analytic behavior in the negative $s$
region, in agreement with the prediction from chiral perturbation amplitudes in
its validity region. The analysis leads again to the conclusion that a genuine
$N^*(890)$ resonance exists.
