The invention relates to an improvement to finishing machines that are used to orient objects. According to the invention, the finishing machine comprises a hopper (4) for receiving loose objects, such as lids (5), and an endless belt (3) for extracting the lids from the hopper (4). The belt (3) moves vertically upwards with the lids (5) and sorts said 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 (5), comprising: a plate (14) which covers the upper part of the belt (3) and which extends laterally beyond said belt, downstream thereof, in order to support the lids (5) as they are ejected from the grooves (7) in the belt (3); means for ejecting the lids (5) from the grooves (7) and for subsequently conveying same beyond the grooves (7) downstream, said ejection means comprising jets of propellant fluid which pass through the plate (14) by means of an arrangement of eyes (15); and a casing (11) which is disposed on the plate (14) and into which the propellant fluid is introduced and maintained under pressure by a turbine (9), said casing (11) extending over the entire surface of the plate (14). In addition, the downstream part of the casing comprises a routing conveyor (13) with an adjustable height H, which transports the oriented lids (5) towards the use station(s).