An expandable ablation electrode is provided on a catheter constructed to access the heart. When the electrode is introduced to the heart, it is small and suitably flexible to maneuver through the torturous path. However, when the catheter is in place in the heart, the electrode is expansible in diameter to a substantially larger dimension, and is relatively rigid, enabling a large conductive surface to press against the heart tissue with the desired contact pressure. When RF energy is then applied to the electrode it produces a burn lesion of desired large size and depth. This overcomes the limitations to size that have been encountered using conventional rigid electrodes.