The present invention relates to a method of electrochemical polishing of surfaces of titanium or titanium-containing alloys, such as Nitinol. An electrolyte is used that comprises methanesulfonic acid and one or more alkanediphosphonic acids. These alkanediphosphonic acids can optionally be substituted with hydroxy and/or amino groups. A further aspect of the present invention relates to the use of said electrolyte for the electropolishing of titanium or titanium-containing alloys.