An improvement to finishing machines that are used to orient objects. The finishing machine includes a hopper for receiving loose objects, such as lids, and an endless belt for extracting the lids from the hopper. The belt moves vertically upwards with the lids and sorts the lids automatically, such that only correctly-oriented lids are retained. The machine is also equipped with a combined system for ejecting and conveying oriented lids, including: a plate which covers the upper part of the belt and which extends laterally beyond the belt, downstream thereof, in order to support the lids as they are ejected from the grooves in the belt; devices for ejecting the lids from the grooves and for subsequently conveying same beyond the grooves downstream, the ejection devices including jets of propellant fluid which pass through the plate by an arrangement of eyes; and a casing which is disposed on the plate and into which the propellant fluid is introduced and maintained under pressure by a turbine, the casing extending over the entire surface of the plate. In addition, the downstream part of the casing includes a routing conveyor with an adjustable height, which transports the oriented lids toward the use stations.