  We give an explicit description of rational curves in the product of three
copies of complex projective lines, which are transformed into twistor lines in
M. Nagata's example of non-projective complete algebraic variety, viewed as the
twistor space of Eguchi-Hanson metric. In particular, we show that there exist
two families of such curves and both of them are parameterized by mutually
diffeomorphic, connected real 4-dimensional manifolds. We also give a
relationship between these two families through a birational transformation
naturally associated to the Nagata's example.
