  We construct in this article a rough path over fractional Brownian motion
with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm
introduced in \cite{Unt-Holder} to reduce the problem to that of regularizing
tree iterated integrals and (ii) applying the
Bogolioubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization algorithm to
Feynman diagrams representing tree iterated integrals.
