  It has been shown that sufficiently well mixing dynamical systems with
positive entropy have extreme value laws which in the limit converge to one of
the three standard distributions known for i.i.d. processes, namely Gumbel,
Fr\'echet and Weibull distributions. In this short note we give an example
which has a non-standard limiting distribution for its extreme values.
Rotations of the circle by irrational numbers are used and it will be shown
that the limiting distribution is a step function where the limit has to be
taken along a suitable sequence given by the convergents.
