The security unit ensures, by blocking the hydraulic flow, that the rod of a cylinder is held in position. It includes two preferably twinned isolation devices, each mounted on one of the hydraulic lines supplying fluid to a chamber of the cylinder. Each isolation device includes two series-connected ball-check valves allowing the flow in the direction of inlet of the fluid into the respective chamber; and a longitudinal, separate rod, inserted between the balls but not linked thereto, and capable of being slidably guided towards each of the balls and driving same. The rod is too short to contact both balls simultaneously when the two valves are closed; but it is sufficiently long to push the ball of the second valve, thereby causing it to open, when it slides under the pushing action of the ball of the first valve upon the latter being controlled to be opened.