A method for manufacturing a curved composite casing for a turbomachine, notably for a low-pressure compressor of an aircraft turbojet engine, includes the following sequence of steps: (a) draping a preform by automatic placement of carbon fibres on a concave form, referred to as a female form; (b) laying a glass-fibre ply on a convex form, referred to as a male form; (c) transferring the preform onto the convex form, covering the glass-fibre ply on the convex form. Step (b) laying includes a phase (α) of laying a metal strip and/or an epoxy profile on the convex form, then a phase (β) of covering the metal strip with the glass-fibre ply.