  We consider the ambitwistor description of $\mathcal N$=4 supersymmetric
extension of U($N$) Yang-Mills theory on Minkowski space $\mathbb R^{3,1}$. It
is shown that solutions of super-Yang-Mills equations are encoded in real
analytic U($N$)-valued functions on a domain in superambitwistor space
${\mathcal L}_{\mathbb R}^{5|6}$ of real dimension $(5|6)$. This leads to a
procedure for generating solutions of super-Yang-Mills equations on $\mathbb
R^{3,1}$ via solving a Riemann-Hilbert-type factorization problem on
two-spheres in $\mathcal L_{\mathbb R}^{5|6}$.
