A system for conveying carcasses or carcass parts of quadruped slaughter animals includes at least one carrier. The carrier includes a first jaw element, which has an engagement face for engaging the carcass or carcass part, a second jaw element, which has an engagement face for engaging the carcass or carcass part. The carrier further includes a tensioning structure, the connection between the first connection zone of the tensioning structure and the first jaw element and the connection between the second connection zone of the tensioning structure and the second jaw element being such that when the jaw elements move relative to each other when receiving a carcass or carcass part in the retaining part of the holding slot, the first connection zone moves along with the first jaw member and the second connection zone moves along with the second jaw member, which movement of the connection zones causes elastic deformation of the tensioning structure, the elastic deformation providing a clamping force to the engagement faces of the jaw elements such that the carcass or carcass part is retained in the holding slot by clamping a part of the carcass or carcass part between the engagement face of the first jaw element and the engagement face of the second jaw element.