The kanji used is translated as 'Dancing' which in way, was supposed to describe their way of fighting.

In Mai-Hime, Nagi frequently referred to them dancing, and in a much later episode, the tradition that led to HiME/element/Child 'festival' started from maidens dancing around a tree for their beloveds. The Academy celebrated that same tradition with the ribbons tied on the circular railing in the main entrance. That is the place the tree once stood.

I'm actually amazed that I remembered all that, since it constitutes to about 3 minutes total of the entire series.