A heart stimulator has a stimulation energy delivering assembly, including at least one lead adapted for implantation in contact with cardiac tissue, and an atrial arrhythmia detector, and a control unit connected to the stimulation energy delivering assembly and to the detector. The control unit controls the stimulation energy delivering assembly to deliver at least one atrial arrhythmia abolishing therapy and, if continued atrial arrhythmia is detected, to deliver antithrombus stimulation energy pulses of lower energy than a defibrillation shock, but with different timing and with sufficient energy for producing atrial contraction for increasing hemodynamic blood transportation away from the atrium and for preventing thrombi formation in the atrium. For a patient suffering from a chronic or paroxysmal non-curable atrial arrhythmia, the control unit controls the stimulation energy delivering assembly to deliver the antithrombus energy without any preceding arrhythmia abolishing therapy.