Abstract: A method of making a catheter is provided. The catheter has an atraumatic portion at the distal end of a catheter having the stiffness and torque resistance required of a catheter such as that suitable for angiographic uses, typically in French sizes on the order of about 2 to about 8. The atraumatic tip portion has a generally co-axially layered structure. An inner layer is made of soft atraumatic polymer, and an outer layer is made of a polymer to impart needed stiffness and torque properties to the catheter. In the preferred embodiment, a portion of the distal tip material of the harder outer layer is removed, thereby exposing the inner, atraumatic material for initial engagement with internal body passageways.