  The functional relation of the Riemann z\^eta function provides us with
neither the nature nor the expression of z\^eta at positive odd numbers. From
the function $F(z)=\frac{z^{-2n}}{e^z-1}$, we find a functional relation
involving $\zeta(4n- 1)$, $\zeta(2p)$ and $\zeta(4n-1-2p)$. It is given by:
\begin{equation}
\zeta(4n-1)=\frac{1}{2n-1}\sum_{p=1}^{2n-2}\zeta(2p)\zeta(4n-1-2p).
\end{equation} $n=2, 3, 4, 5, 6, ...$ From this formula we introduce a new
approach to study the nature of $\zeta$ on these integers.
