  The linear fractional map $ g(z) = \frac{az+ b}{cz + d} $ on the Riemann
sphere with complex coefficients $ ad-bc = 1 $ is and $ a+d = \pm 2 $, then $ g
$ is called {\em parabolic} M\"obius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0}
$ be the solution of the parabolic M\"obius difference equation $ b_{n+1} =
g(b_n) $ for every $ n \in \mathbb{N}_0 $. We show that the sequence $ \{ b_n
\}_{n \in \mathbb{N}_0} $ has no Hyers-Ulam stability.
