A safety device on a rope, comprising a first flange-plate and a movable second flange-plate, a roller mounted on a first spindle integral to the first flange-plate, which presents clearance in the heightwise direction. The movable second flange-plate is equipped: with a securing notch operating in conjunction with the first spindle to block the device in the closed position when the roller is under load, and with a latch actuated by control means to perform unlatching of the latter enabling opening of the second flange-plate when the device is no longer under load.