  In this note we prove that the moduli space of rank $2n$ symplectic instanton
bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is
affine. This result was not known even in the case $n=1$, where the real
instanton bundles correspond to self dual Yang Mills $Sp(1)$-connections over
the 4-dimensional sphere. The result is proved as a consequence of the
existence of an invariant of the multidimensional matrices representing the
instanton bundles.
