  We give a new approach to the symmetries of the Painlev\'e equations
$P_{V},P_{IV},P_{III}$ and $P_{II}$, respectively. Moreover, we make natural
extensions to fourth-order analogues for each of the Painlev\'e equations
$P_{V}$ and $P_{III}$, respectively, which are natural in the sense that they
preserve the symmetries.
