Curved stiffener for a turbomachine cowl composed of a resin-impregnated fibrous reinforcement, including a stack of a plurality of layers of fibers stacked along the thickness direction and extending on the entire width of the fibrous reinforcement, each layer of fibers having a plurality of fibers parallel to each other extending along a direction inclined relative to the length direction, the fibers of two consecutive layers of fibers along the thickness direction have directions inclined relative to each other, and the layers of fibers are sewn together by sewing threads extending along the length direction, the fibrous reinforcement includes a layer of reinforcing fibers having a plurality of fibers parallel to each other extending along the length direction, the layer of reinforcing fibers extending at least on the central part, over a width smaller than the width of the fibrous reinforcement.