Abstract: We analyse the effect of the re-scaling of the basic auxiliary fields in  E.Ivanov and B.Zupnik approach to self-dual nonlinear electrodynamics. It is turned out that such re-scaling is quite useful helping to construct new self-dual Lagrangians explicitly .  We also discuss very simple and straightforward procedure for constructing of self-dual actions which based only on assumption that the linear realization of duality symmetry exists. Finally, we present two new self-dual Lagrangians.