  In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave
a classification of linear Nambu structures, and obtained linearization results
for Nambu structures with a nondegenerate linear part. There was a case left
open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of
Nambu structures with a Type 1 hyperbolic linear part which satisfies a natural
signature condition. In this paper, we will show that such hyperbolic Nambu
structures are also smoothly linearizable. We will also give a strong version
of the analytic linearization theorem in the analytic case, improving a result
obtained in \cite{DufourZung-Nambu1999}.
