In a self-propelled cold milling machine, in particular cold milling machine, for working ground surfaces, with a milling drum supported at a machine frame, no less than one conveying device arranged at the machine frame which accepts the milled-off material from the milling drum and discharges said milled-off material, in conveying direction, at a discharge end along a parabolic trajectory onto a point of discharge, it is provided for the following features to be achieved: that the conveying device comprises a shielding device at the discharge end, where said shielding device shields the material milled off and leaving the conveying device without influencing the parabolic trajectory on a part of the path to the point of discharge at least by means of lateral sections.