A method is claimed for the production of a drawn wire, notably a pneumatic reinforcing wire with a diameter of less than 0.3 mm, by drawing from a base machine wire with a diameter greater than 5 mm or from a previously drawn wire based on a stainless steel with a balanced composition conforming to given individual limits for its various components. The steel has set limits for its content of oxide inclusions and its composition conforms to given relationships between its components. The base wire is subjected to a wire drawing operation satisfying the following conditions:- a) a cumulative rate of deformation greater than 6; b) keeping the wire, during the wire drawing operation and between wire drawing operations, at a temperature of less than 650 degrees C, and preferably at a temperature of less than 600 degrees C, without reheating between the wire drawing passes. The stainless steel used in this method is also claimed.
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