  We consider ground state solutions of the critical Lane-Emden system
\[\begin{cases} -\Delta u = v^p &\text{in } \mathbb{R}^n,\\ -\Delta v = u^q
&\text{in } \mathbb{R}^n,\\ u,v >0\ &\text{in } \mathbb{R}^n, \end{cases}\]
where $n \ge 3$ and $p,q>0$ and $(p,q)$ belongs to the critical hyperbola
$\frac{1}{p+1} + \frac{1}{q+1} = \frac{n-2}{n}.$ We prove that they are
non-degenerate when either $(p,q)$ is close to $(1,{n+4\over n-4})$ (if
$n\ge5$) or $(p,q)$ is close to $({n+2\over n-2},{n+2\over n-2})$ (if $n\ge3$).
