Stopping Antihypertensive Treatment amOng Hypertensive Patients in Primary Care (STOP-Trial)

HBPM should be performed by the patients twice a day for 7 consecutive days before each visit (ESH protocol), using a device clinically tested (ESH/international protocol). At baseline (visit 1), for the patients included, the antihypertensive treatment will be stopped in 3 consecutive days (half dose then interruption), over a maximum period of 12 months corresponding to the length of the participation and the monitoring of the patients. Follow-up visits at day 30 (visit 2), day 90 (visit 3), day 180 (visit 4), day 270 (visit 5) and day 360 (visit 6). Will be performed at each visit: * Calculation of the average of HBPM values by the investigator * Measurements of office blood pressure (average of 3 consecutive measurements) * SF 36 scale at baseline (visit 1) and day 360 (visit 6) * During follow-up, the investigator will be free at any time to reintroduce an antihypertensive treatment if the average of HBPM values is greater than or equal to 135/85 mmHg on two consecutive visits, or greater than or equal to 155/95 mmHg regardless of the visit and regardless of the office blood pressure level. At the end of study, the recovery of an antihypertensive treatment by the patients will be left to the discretion of the investigator.