  We perform a recursive reduction of one-loop $n$-point rank $R$ tensor
Feynman integrals [in short: $(n,R)$-integrals] for $n\leq 6$ with $R\leq n$ by
representing $(n,R)$-integrals in terms of $(n,R-1)$- and
$(n-1,R-1)$-integrals. We use the known representation of tensor integrals in
terms of scalar integrals in higher dimension, which are then reduced by
recurrence relations to integrals in generic dimension. With a systematic
application of metric tensor representations in terms of chords, and by
decomposing and recombining these representations, we find the recursive
reduction for the tensors. The procedure represents a compact, sequential
algorithm for numerical evaluations of tensor Feynman integrals appearing in
next-to-leading order contributions to massless and massive three- and four-
particle production at LHC and ILC, as well as at meson factories.
