  Let $MI_{Simp,P^{2n+1}}(k)$ be the moduli space of stable symplectic
instanton bundles on $P^{2n+1}$ with second Chern class $c_2=k$ (it is a closed
subscheme of the moduli space $MI_{P^{2n+1}}(k)$), We prove that the dimension
of its Zariski tangent space at a special (symplectic) instanton bundle is
$2k(5n-1)+4n^2-10n+3, k\geq 2$. It follows that special symplectic instanton
bundles are smooth points for $ k \leq 3 $
