second current source 56 at contact points c and d after the passing through the second electrolyte bath abrasive wire 3 is obtained it may be stored in the form of a coil 68 as already indicated device 2 is described in further detail in the patent application filed under number fr 12 53017 as shown in fig2 abrasive wire 3 according to the invention has a core 4 coated with a first binder layer 10 partially covering abrasive particles 6 according to this specific embodiment the abrasive wire further comprises a second binder layer 12 covering abrasive particles 6 this second binder layer advantageously has a better abrasion resistance than the first layer on the other hand the second binder layer 12 is advantageously less hard and more ductile than the first layer 10 covering the steel core 4 the two layers 10 and 12 and abrasive particles 6 form external coating 8 of abrasive wire 3 according to a specific embodiment abrasive particle 6 comprises an abrasive grain 16 covered with a film 18 fig3 the film is advantageously made of a magnetic material to ease the electrodeposition of the particles on steel core 4 indeed the electrodeposition of the external coating is advantageously implemented in the presence of magnetic particles a plurality of abrasive wires examples 1 9 have been prepared from a steel core in the hardened state the steel core comprises 0 8 of carbon it has a 0 12 millimeter diameter 1 degreasing the steel core in an alkaline medium 2 pickling the steel core in an acid medium 3 electrodeposition by passing the steel core in a first electrolyte bath b 1 comprising abrasive particles to form.