  Flavor changing neutral currents coming from a new non-universal neutral
Gauge-Boson and from the non-unitary quark mixing matrix for the
$SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ model with right handed neutrinos are
studied. By imposing as experimental constraints the measured values of the 3x3
quark mixing matrix, the neutral meson mixing, and the bounds measured values
for direct flavor changing neutral current processes, the largest mixing of the
known quarks with the exotic ones can be established, with new sources of
flavor changing neutral currents being identified. Our main result is that for
a $|V_{tb}|$ value smaller than one, large rates of rare top decays such as
$t\to c\gamma$, $t\to cZ$, and $t\to cg$ (where g stands for the gluon field)
are obtained; but if $|V_{tb}|\approx 1$ the model can survive present
experimental limits only if the mass of the new neutral Gauge Boson becomes
larger that 10 TeV.
