  We study vacuum solutions of five-dimensional Einstein equations generated by
the inverse scattering method. We reproduce the black ring solution which was
found by Emparan and Reall by taking the Euclidean Levi-Civita metric plus
one-dimensional flat space as a seed. This transformation consists of two
successive processes; the first step is to perform the three-solitonic
transformation of the Euclidean Levi-Civita metric with one-dimensional flat
space as a seed. The resulting metric is the Euclidean C-metric with extra
one-dimensional flat space. The second is to perform the two-solitonic
transformation by taking it as a new seed. Our result may serve as a stepping
stone to find new exact solutions in higher dimensions.
