  The Dirac quasinormal modes (QNMs) of the Kerr-Newman black hole are
investigated using continued fraction approach. It is shown that the
quasinormal frequencies in the complex $\omega$ plane move counterclockwise as
the charge or angular momentum per unit mass of the black hole increases. They
get a spiral-like shape, moving out of their Schwarzschild or
Reissner-Nordstr\"om values and "looping in" towards some limiting frequencies
as the charge and angular momentum per unit mass tend to their extremal values.
The number of the spirals increases as the overtone number increases but
decreases as the angular quantum number increases. It is also found that both
the real and imaginary parts are oscillatory functions of the angular momentum
per unit mass, and the oscillation becomes faster as the overtone number
increases but slower as the angular quantum number increases.
