A method of machining an attachment flange of an aircraft turbomachine case, the method also including a system to machine the two opposite surfaces of the flange, and including a shape follower machining module, this module being designed to follow the shape of the flange and including a first structure equipped with a first machining tool, and a second structure equipped with a second machining tool, the flange fitting between the structures such that its two opposite surfaces are machined by tools, the module also including shape follower elements carried by the structures; and a device to drive movement of the machining module along a circumferential direction of the flange.