In a self-propelled construction machine, in particular cold milling machine, recycler or surface miner, for working ground surfaces, comprising a milling drum supported at a machine frame and a conveying device arranged at the machine frame which accepts the milled-off material from the milling drum during the working operation and, on a continuously revolving first transport belt, unloads it, in conveying direction, onto a point of discharge at a discharge end along a parabolic trajectory, it is provided for the following features to be achieved: as a minimum, the last section of the conveying device as seen in conveying direction comprises no less than one continuously revolving cover belt arranged above the transport belt, said cover belt extending essentially parallel to the transport belt and resting against the milled-off material on the transport belt at least in a partial section of the length of the transport belt.
