An intravascular device for the formation of linear lesions which has particular utility in the treatment of atrial fibrillation and flutter. The intravascular device has an outer delivery member with a distal section which has an elongated opening and a support element coextending with the opening. An EP device having a plurality of electrodes on its distal section is slidably disposed within the inner lumen of the delivery member but it is secured by its distal end within the distal extremity of the delivery member at least while in operation. In this manner an axial force in the proximal direction on the proximal extremity of the EP device, which extends out of the patient during the procedure, will cause the distal shaft section of the EP device to arch outwardly out of and away from the distal section of the delivery shaft along an inner side of the curved distal section and engage the surface of the patient's heart chamber. RF electrical energy delivered to the electrodes on the distal shaft section of the EP device will form a linear lesion which terminates the fibrillation or flutter.