  The Kerr-Schild pencil of metrics $\tilde g_{ab}=g_{ab}+V l_al_b$, with
$g_{ab}$ and $\tilde g_{ab}$ satisfying the vacuum Einstein equations, is
investigated in the case when the null vector $l$ has vanishing twist. This
class of Kerr-Schild metrics contains two solutions: the Kasner metric and a
metric wich can be obtained from the Kasner metric by a complex coordinate
transformation. Both are limiting cases of the K\'ota-Perj\'es metrics. The
base space-time is a pp-wave.
