  We study the equality of the extremal Betti numbers of the binomial edge
ideal $J_G$ and those of its initial ideal ${\rm in}(J_G)$ of a closed graph
$G$. We prove that in some cases there is an unique extremal Betti number for
${\rm in}(J_G)$ and as a consequence there is an unique extremal Betti number
for $J_G$ and these extremal Betti numbers are equal
