  A numerical approach to compute tensor integrals in one-loop calculations is
presented. The algorithm is based on a recursion relation which allows to
express high rank tensor integrals as a function of lower rank ones. At each
level of iteration only inverse square roots of Gram determinants appear. For
the phase-space regions where Gram determinants are so small that numerical
problems are expected, we give general prescriptions on how to construct
reliable approximations to the exact result without performing Taylor
expansions. Working in 4+epsilon dimensions does not require an analytic
separation of ultraviolet and infrared/collinear divergences, and, apart from
trivial integrals that we compute explicitly, no additional ones besides the
standard set of scalar one-loop integrals are needed.
