The present invention relates to a rotary kiln for burning carbonate-containing material, in particular limestone or dolomite, including a rotary tube having an inlet end for feeding the material to be burned and an outlet end for discharging the burnt material, and a burner unit arranged in the region of the outlet end, the rotary tube having an inlet zone at its inlet end and an outlet zone at its outlet end, a preheating zone and a combustion zone being arranged between the inlet zone and outlet zone in the direction of transport of the material. The rotary kiln is characterized according to the invention in that at least one projection is arranged in the outlet zone of the rotary tube, the at least one projection having a contour tapering in the direction of rotation of the rotary tube. The present invention further relates to a method for burning carbonate-containing material, in particular limestone or dolomite.