A terrain avoidance method and system for an aircraft includes a collision alarm device and an auto-pilot device including a first determination unit for determining a climbing order with optimal slope for the aircraft, a checking unit for checking whether a first altitude gain at the relief, by applying the optimal slope climbing order, is sufficient for clearing said relief, a finding unit for finding if at least one heading variation value exists, for which the corresponding altitude gain is sufficient to clear the relief, and a switching and calculating unit for applying to the aircraft, if the first altitude gain is sufficient, an optimal slope climbing order with an order to maintain the current heading and, if the first altitude gain is insufficient, a particular climbing order sufficient to clear the relief, with a heading order which corresponds to the selected heading variation value.