Apparatus for mapping a wall of a heart forming a chamber in the heart comprising a guiding catheter having a lumen extending therethrough and a mapping catheter having a shaft that is slidably mounted in the lumen of the guiding catheter. A basket assembly is provided and is comprised of a plurality of circumferentially spaced-apart longitudinally extending arms having proximal and distal extremities. The proximal extremities of the arms are secured to the distal extremity of the shaft of the mapping catheter. Each of the arms includes a member formed of a material having a recoverable strain in excess of 1% and has an outwardly bowed shape memory. At least one electrode is provided on each of the arms. Conductors connected to the electrodes are carried by the arms.