  We present a consistent truncation, allowing us to obtain the first degree
birational transformation found by Okamoto for the sixth Painlev\'e equation.
The discrete equation arising from its contiguity relation is then just the sum
of six simple poles. An algebraic solution is presented, which is equivalent to
but simpler than the Umemura solution. Finally, the well known confluence
provides a unified picture of all first degree birational transformations for
the lower Painlev\'e equations, ranging them in two distinct sequences.
