a distal tip member such as tip member 24 may be provided in the embodiment having an outer sleeve member 40 as for example with a tip member not shown butt joined to the distal end of the inner tubular member 15 with outer sleeve member 40 sealingly surrounding the butt joint in a method of making a balloon catheter of the invention the break 25 45 is formed in the sidewall of the outer sheath member i e the distal skirt section 21 or the outer sleeve member 40 preferably by mechanically cutting through the wall of the outer sheath member with a cutting blade however break 25 45 may alternatively be formed by a variety of suitable methods including other methods of material removal such as laser cutting prior to being bonded to the catheter shaft the outer sheath member is a tubular member with the break 25 in a wall thereof and with a lumen therein configured to receive the catheter shaft therein so that the outer sheath member can be placed in surrounding relation to the shaft and subsequently bonded thereto fig6 illustrates the distal skirt section 21 with the spiraling break 25 in the wall thereof before the catheter shaft 11 is.