  We study birational transformations belonging to Galois points. Let $P$ be a
Galois point for a plane curve $C$ and $G_P$ be a Galois group at $P$. Then an
element of $G_P$ induces a birational transformation of $C$. In general, it is
difficult to determine when this birational transformations can be extended to
a Cremona (or projective) transformation. In this article, we shall prove that
if the Galois group is isomorphic to the cyclic group of order three, then any
element of the Galois group has an expression as a de Jonqui\`{e}res
transformation. In particular, they can be extended to Cremona transformations.
