Beverage preparation machine comprising a body (2), a movable steam nozzle (7) connected to the body by a moving device (13), a beverage preparation area (10) in which a cup can be placed, and a cleaning area in which is disposed a rinsing container (12). The moving device (13) moves the nozzle (7) between the preparation and cleaning areas. The machine also includes a cleaning product outlet (56) that can be moved between a dispensing position located in the cleaning area for dispensing product into the container (12), and a storage position located outside the cleaning area. The cleaning product outlet (56) is connected to the moving device (13) so as to place this outlet in the storage position when the nozzle (7) is in the cleaning area.