 Heart failure is a condition that occurs when the heart muscle weakens and no longer contracts normally. Half of these patients have an irregularity of heart rhythm called atrial fibrillation AF. Patients with both heart failure and AF spend more time in hospital, and die earlier than those with heart failure alone. AF is difficult to treat with conventional methods in patients with heart failure. Radiofrequency ablation is a new technique used to cure AF. The investigators aim to establish if radiofrequency ablation for atrial fibrillation in patients with advanced heart failure can result in marked improvement in the function of the heart. 