A process for the treatment of atrial arrhythmia by use of ablation procedures comprising circumferential ablation of vessels, particularly pulmonary veins, associated with the left atrium of the heart. Also medical devices for such process including a pair of balloons secured to a catheter with one balloon located within the other balloon and an ablation catheter located within one of the balloons, which devices are used for the formation of a circumferential ablation lesion in the pulmonary vein.