A catheter for measuring electrical activity and ablating tissue is provided. The catheter comprises an elongated generally-tubular catheter body. A non-retractable electrode assembly is mounted at the distal end of the catheter body. The electrode assembly comprises a generally tubular ablation electrode formed of a material having shape-memory having a generally straight exposed region and at least one irrigation port in the exposed region through which fluid can pass from the inside to the outside of the ablation electrode. The exposed region is generally transverse to the catheter body. The electrode assembly further comprises a tip at the distal end of the electrode assembly comprising a generally ball-shaped exposed region. First and second distal mapping electrodes are mounted distal to the exposed region of the ablation electrode. At least the first distal mapping electrode, and optionally the second distal mapping electrode, is incorporated into the generally ball-shaped exposed region of the tip. The catheter further comprises an infusion tube extending through the catheter body and having a distal end in fluid communication with the proximal end of the ablation electrode.