Beverage preparation machine comprising a body 2 having a facade, a beverage preparation area (10) delimited on one side by the facade 3, in its upper part by beverage outlets, and in its lower part by a cup rest 8, and a movable steam nozzle 7 connected to the body by a moving device. The body includes a housing 3c defining a cleaning area 25, in which is disposed a rinsing container 12 having a top opening 22 and including a draining device 23, and in which the movable nozzle 7 is driven in a vertical movement by the moving device so that its free end 7a enters the container 12 through its top opening.