An apparatus for transferring while turning upside down a piece of meat such as loins from a supply surface on which the loins are in one position to a receiving conveyor on which a plurality of saddles are mounted at regular intervals to receive the loins in another upside down position. The apparatus has an L-shaped rack for receiving the loins from the supply surface. This rack is pivotable between a stopping position and a delivering position in which its surface acts as an extension of the supply surface on which the loins may slide to reach the saddles. An inverting member is mounted onto the rack and pivotably movable therewith between the stopping and delivering positions. This inverting member is shaped and positioned in such a manner as to extend in the same plane or under the supply surface when the rack is in its stopping position in order to collect the loin that is on the supply surface, and then to cause it to turn upside down onto the receiving surface while the rack is rotating down into its delivering position.