A method for the surface preparation of devices made of titanium or titanium alloys, zirconium, zirconia, alumina or zirconia/alumina compounds, stainless steels for medical use and cobalt-base superalloys for medical use form the object of the finding; said devices being implantable in the human body or in animals and attached extracorporeal parts made with the same materials, particularly for dental and orthopedic implantology. The implantable device is thus treated: it is provided to expose at least one portion of the surface of said device to a solution comprising hydrofluoric acid, phosphoric acid, at least one surfactant substance and water; the exposure occurs for a time period and in conditions sufficient to provide the surface of the implant with the desired surface roughness and the formation of self-induced surface titanium dioxide, maintaining the structural integrity of the device and without altering the centesimal measurement size. The surface thus treated is rinsed with demineralized water and ultrasounds in order to prevent metalosis phenomena. On the extraosseous parts complementary to the devices to be implanted in the bone, nanometer particles of mineral trace elements are applied, smaller than 20 nanometers, and in particular 99.9% pure silver having self-hygienizing function and clinging to the surfaces treated with the above-described method, without the aid of adhesives.