We consider random finite permutations and prove the following version of Thoma's theorem in \cite{Th}: Random finite permutations which are class functions satisfy a new integration by parts formula iff they are given by a certain Ewens-Suto process. The main source of inspiration for the results in this note is the fundamental work of Andras Suto \cite{S}, from which some results are reestablished here again in the present point process approach.