  We provide a complete system of invariants for the formal classification of
complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the
orbits of a regular vector field. We reduce the formal classification problem
to solve a linear differential equation. Then we describe the formal
invariants; their nature depends on the position of the fixed points set $Fix
\phi$ with respect to the regular vector field preserved by $\phi$. We get
invariants specifically attached to higher dimension ($n \geq 3$) although
generically they are analogous to the one-dimensional ones.
