  We calculate analytically the asymptotic form of quasi-normal modes of
perturbations of arbitrary spin of a Schwarzschild black hole including
first-order corrections. We use the Teukolsky equation which applies to both
bosonic and fermionic modes. Remarkably, we arrive at explicit expressions
which coincide with those derived using the Regge-Wheeler equation for integer
spin. Our zeroth-order expressions agree with the results of WKB analysis. In
the case of Dirac fermions, our results are in good agreement with numerical
data.
