A thrust reverser with grids includes a jet engine pylon, a one piece cowl either directly or indirectly slidably mounted on the jet engine pylon between a direct jet position and a reverse jet position, and a system for locking this cowl on a beam. The system has a single tertiary lock, which is positioned on one side of the jet engine pylon being capable of locking a corresponding upper edge of the cowl. In addition, the tertiary lock includes a locker to lock the cowl, a blocker for blocking the locker, and a position detector in order to detect the position of the locker. The system further includes another detector to detect proper closing of the other upper edge of the cowl.