A method for producing a curved section piece from a rectilinear preform of preimpregnated fiber layers includes stacking layers on a deformable mandrel and winding the mandrel and bending the stacked layers on a bending tool on a rotation axis in a single phase and polymerizing the bent layers. The section piece includes a stack of N layers, at least a first portion of which is placed in a plane perpendicular to the rotation axis (X) and at least one second portion parallel to the axis (X) including at least one layer of fibers oriented at 0° along the length of the perform. The N fiber layers are stacked on the mandrel. A neutral fiber is placed on a portion of the mandrel closer to the rotation axis (X) than the last layer of fibers oriented at 0° stacked on the 0second portion parallel to the rotation axis (X).