Method of and system for automatically deboning poultry breast caps containing meat and a skeletal structure to obtain breast fillets. The method includes providing a mandrel with a plane of symmetry in a vertical orientation and supporting a breast cap with its skeletal structure including a keel bone on top of the mandrel. The breast cap being held to the mandrel with the keel bone aligned with the plane of symmetry. By moving the mandrel through a conveying path extending through a substantially horizontal plane in a direction of travel it passes a cutting implement of a breast cutter engaging the meat along the keel bone. The cutting implement causes at least one incision along the area where the meat is attached to the keel bone and a breast fillet remover downstream of the breast cutter engages between the skeletal structure and the meat and separates the meat as a pair of single fillets from the skeletal structure. The arrangement is such that the mandrel moves through the conveying path with the plane of symmetry aligned with the direction of travel.