  The neutrino quasinormal modes of the Reissner-Nordstr\"om (RN) black hole
are investigated using continued fraction approach. We find, for large angular
quantum number, that the quasinormal frequencies become evenly spaced and the
spacing of the real part depends on the charge of the black hole and that of
the imaginary part is zero. We then find that the quasinormal frequencies in
the complex $\omega$ plane move counterclockwise as the charge increases. They
get a spiral-like shape, moving out of their Schwarzschild value and ``looping
in" towards some limiting frequency as the charge tends to the extremal value.
The number of the spirals increases as the overtone number increases but it
decreases as the angular quantum number increases. We also find that both the
real and imaginary parts are oscillatory functions of the charge, and the
oscillation becomes faster as the overtone number increases but it becomes
slower as the angular quantum number increases.
