For separating flat articles from a lying stack of articles, each foremost article of the stack is conveyed away one after the other in an upwards direction. For making such separation applicable also for mechanically relatively unstable articles, a preparatory step is implemented prior to the step of conveying-away upwards. In this preparatory step each foremost article of the stack is gripped, then separated from the front end of the stack in a direction essentially perpendicular to the main surfaces of the stacked articles and simultaneously or immediately afterwards accelerated upwards. Only when the article has a speed component in upwards direction of approximately the order of magnitude of the conveying-away speed is the article transferred to the conveying-away means. The preparatory step is carried out with a suction device that moves on a suction device track.