  Collisions at the LHC produce many-particle final states, and for precise
predictions the one-loop $N$-point corrections are needed. We study here the
tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive
solution by Binoth et al. expresses $N$-point Feynman integrals of rank $R$ in
terms of $(N-1)$-point Feynman integrals of rank $(R-1)$ (for $N\ge 6$). We
show that the coefficients can be obtained analytically from suitable
representations of the metric tensor. Contractions of the tensor integrals with
external momenta can be efficiently expressed as well. We consider our approach
particularly well suited for automatization.
