A system for ablating or monitoring a zone of the heart, includes a system to measure the heart electrical activity a phased array for generating a beam of focussed ultrasound signals on a targeted zone of the heart an imaging system determining an image of a transcostal wall projected in an image plane of the phased array by taking into consideration a position and direction of the phased array and making it possible to deactivate elements of the phased array in accordance with the position of the elements with regard to the position of the projected image of the transcostal wall a positioning system to control the position of a focussed zone of a beam of focussed ultrasound signals on the targeted zone, a monitoring system to measure a temperature and tissue deformation in the targeted zone and a device for measuring a level of cavitation in the targeted zone.
