A method for manufacturing a preform has a non-developable end shape having, about a longitudinal axis (A), an end overall radius of curvature (R2), and, in at least a longitudinal section, curved segments forming bending radii linking straight segments. The method includes a step of depositing successive layers giving the preform an initial substantially rotational shape having, about the longitudinal axis (A), an initial overall radius of curvature, then a step of deploying the preform by increasing the initial overall radius of curvature until the end overall radius of curvature is reached (R2), in order to close the bending radii of the curved segments.