An improved guidewire for advancing a catheter within a body lumen which has a high strength proximal portion, a distal portion formed of superelastic alloy and a connector formed of superelastic alloy to provide torque transmitting coupling between the distal end of the proximal portion and the proximal end of the distal portion. The superelastic alloy elements are preferably cold worked and then heat treated at a temperature well above the austenite-to-martensite transformation temperature, while being subjected to longitudinal stresses equal to about 5 to about 50% of the room temperature yield stress to impart to the metal a straight “memory.” The guiding member using such improved material exhibits a stress induced austenite-to-martensite phase transformation at an exceptionally high constant yield strength of at least 70 ksi for solid members and at least 50 ksi for tubular members with a broad recoverable strain of at least about 4% during the phase transformation.