The process for manufacturing a surgical needle produced from a wire of hyper-elastic or super-elastic alloy comprising an Ni-Ti alloy base, consist: • in carrying out a shaping of the curved profile of the needle at low temperature or at ambient temperature in an appropriate support; • in subjecting the needle in its support to a heat treatment in order to memorize the imposed curved profile geometry; • in cleaning the needle by means of a chemical pickling of electrochemical or electrolytic polishing type or a chemical solution for removing the oxide layer deposited on the needle during the heat treatment thereof.