  Adding a topological theta term to the action of $\mathcal{N}{=}\,1$ $D{=}4$
super Yang-Mills theory modifies its Nicolai map. For the BPS value of the
theta angle a chiral version of the map emerges, which allows for a
considerable simplification compared to the non-chiral formulation. We exhibit
these improvements to all orders in perturbation theory and compute the map to
fourth order in the coupling on the Laudau-gauge hypersurface. The second-order
contribution vanishes, and antisymmetrizations are more manifest. All checks
are verified to third order.
