  We consider the Hamiltonian system with Neumann boundary conditions: \[
-\Delta u + \mu u=v^{q }, \quad -\Delta v+ \mu v=u^{p} \quad \text{ in
$\Omega$}, \qquad
  u, v >0 \quad \text{ in $\Omega$,} \qquad \partial_\nu u= \partial_\nu v=0
\quad \text{ on $\partial \Omega$, } \] where $\mu >0$ is a parameter and
$\Omega$ is a smooth bounded domain in $\mathbb R^N .$
  When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) +
N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the
mean curvature achieves its minimum and negative value.
