  We consider the phase separation problem for the one--dimensional
ferromagnetic Ising model with long--range two--body interaction,
$J(n)=n^{-2+\a}$ where $n\in \N$ denotes the distance of the two spins and $
\alpha \in ]0,\a_+[$ with $\a_+=(\log 3)/(\log 2) -1$. We prove that given
$m\in ]-1,+1[$, if the temperature is small enough, then typical configuration
for the $\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization
of the order $m$ are made of a single interval that occupy almost a proportion
$\frac{1}{2}(1-\frac{m}{m_\b})$ of the volume with the minus phase inside and
the rest of the volume is the plus phase, here $m_\b>0 $ is the spontaneous
magnetization.
