Decisive modifications are proposed to a cutting system reducing cutting losses and having a floating disk, in order to improve the efficiency of the system. The lower finger (1) cuts at the lower level and has a tip pointing upwards to prevent the finger from entering the ground; weeds passing past the lower finger pass over the upper finger (3), the accumulation of branches between the fingers being thus prevented. The upper finger (3) has a guard (4) that prevents grains from dropping out of the cutting platform, and the guard is also used to mount two bearings which act to orient the cutter bar (2).