A method for operating a tray conveying apparatus, wherein a tray edge of a tray to be destacked is guided in contact with and along a support until the tray has been deposited on a conveying unit positioned therebelow. An apparatus for destacking and further conveying trays that may comprise a destacker for destacking trays, wherein the destacker may also comprise a frame for accommodating at least one tray stack and a plurality of destacking screws configured to be operated in a respective direction of rotation. Each destacking screw may comprise a helically configured spiral or groove with a support. A conveying unit may be positioned below the destacker and used for receiving and transporting the destacked trays from the destacker.