A primary structure of an aircraft pylon, which comprises upper and lower spars, right-hand and left-hand lateral panels, transverse reinforcers that are disposed in transverse planes and, each have a square or rectangular contour and at least one sole to which the upper and lower spars and the right-hand and left-hand lateral panels are fastened. At least one of the transverse reinforcers of the primary structure has first and second link rods that are oriented along diagonals of the transverse reinforcer, and connecting systems that each connect first and second ends of the first and second link rods to the sole or to one of the soles.