  In the note we consider an iterative generalisation of the rejection sampling
method. In high energy physics, this sampling is frequently used for event
generation, i.e. preparation of phase space points distributed according to a
matrix element squared $|M|^2$ for a scattering process. In many realistic
cases $|M|^2$ is a complicated multi-dimensional function, so, the standard von
Neumann procedure has quite low efficiency, even if an error reducing
technique, like VEGAS, is applied. As a result of that, many of the $|M|^2$
calculations go to ``waste''. The considered iterative modification of the
procedure can extract more ``unweighted'' events, i.e. distributed according to
$|M|^2$. In several simple examples we show practical benefits of the technique
and obtain more events than the standard von Neumann method, without any extra
calculations of $|M|^2$.
