A method and system for lysing a patient's heart tissue causing or involved with arrhythmia which includes an intravascular catheter with a relatively inelastic occlusion balloon on the distal end of the catheter which is inflated to block an artery or vein of the patient's heart so than when lysing fluid such as an ethanol solution is discharged from the distal port in the catheter the inflated balloon prevents the proximal refluxing of lysing medium into undesirable areas of the patient's heart. The inelastic balloon is configured to be inflated to a diameter of about 0.7 to about 1.3, preferably about 0.8 to about 1.2, times the diameter of the blood vessel in which the balloon is to be inflated so as to effectively occlude the passageway without damaging the wall of the blood vessel. The working length of the balloon is less than about 1.5 cm, preferably less than 0.75 cm.