  In a paper (math.DG/0403528) we obtained explicit examples of Moishezon
twistor spaces of some compact self-dual four-manifolds admitting a non-trivial
Killing field, and also determined their moduli space. In this note we
investigate minitwistor spaces associated to these twistor spaces. We determine
their structure, minitwistor lines and also their moduli space, by using a
double covering structure of the twistor spaces. In particular, we find that
these minitwistor spaces have different properties in many respects, compared
to known examples of minitwistor spaces. Especially, we show that the moduli
space of the minitwistor spaces is identified with the configuration space of
different 4 points on a circle divided by the standard PSL(2, R)-action.
