Abstract: The invention concerns an arrangement for machining a valve seat (1a) in a valve housing (1). The housing has a circular opening (1d) which is concentric with the seat (1a) and about which is a flat annular surface (1e). The arrangement comprises a support (2) arranged such that it is held by the valve housing (1) and such that, in an axial direction perpendicular to the plane of the annular surface (1e), it holds a tool pillar (3). At its distal end the tool pillar (3) has a machining tool (4). The support (2) comprises firstly a main part with three wings uniformly distributed about the tool pillar (3). Each wing comprises a first wing part (2b) which is operatively connected to the first wing part so that these wing parts (2a, 2b) can slide relative to each other along the sliding surface. Members (2b2, 2b3, 2b4, 2b5) are provided for detachably securing the wing parts (2a, 2b) relative to each other and the support (2) relative to the valve housing (1).