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We present a consistent truncation, allowing us to obtain the first degreebirational transformation found by Okamoto for the sixth Painlev\'e equation.The discrete equation arising from its contiguity relation is then just the sumof six simple poles. An algebraic solution is presented, which is equivalent tobut simpler than the Umemura solution. Finally, the well known confluenceprovides a unified picture of all first degree birational transformations forthe lower Painlev\'e equations, ranging them in two distinct sequences.Comment: LaTex 2e. To appear, J. Phys. A, Special issue SIDE I

First-degree birational transformations of the Painlevé equations and their contiguity relations