In a self-propelled construction machine, specifically, a road milling machine, a surface miner or a recycler, for milling a ground surface, comprising a machine frame with a longitudinal axis, comprising a chassis with wheels or tracked ground-engaging units which support the machine frame, comprising a controller for the travelling and milling operation, comprising a height-adjustable working drum, comprising a slewable transport conveyor arranged in front of or behind the working drum as seen in the direction of travel of the milling machine with a discharge end from which worked-off milling material is dischargeable onto a point of impingement on a loading surface of a means of transport, wherein the transport conveyor is slewable about, as a minimum, a first slewing axis extending essentially orthogonal to the machine frame laterally under a slewing angle, wherein the controller comprises a control system which controls, as a minimum, the slewing angle of the transport conveyor automatically in the trave
