A fluid dispenser member having a dispensing wall defining an outside surface and inside surface, the wall being provided with a through dispensing orifice connecting the inside surface to the outside surface. The inside surface forming a leaktight slide cylinder for a piston suitable for moving in leaktight contact inside the cylinder for selectively unmasking the dispensing orifice. The piston forming a wall element of a fluid chamber inside which fluid is selectively put under pressure. The inside surface, at the slide cylinder, forming a fluid swirl system immediately upstream from the dispensing orifice. The dispensing wall is formed by a substantially cylindrical skirt further provided with a guide wall defining an inside surface whose inside diameter is greater than the inside diameter of the slide cylinder.