A method of generating an output flow of containers wherein the containers are in a vertical position with the same orientation by orienting containers included in an input flow of containers advancing in a given direction (X B), wherein the containers in said input flow have four possible conditions of arrival corresponding to a first sense of advance with a neck part of the containers facing forwards or a second sense of advance with the neck part of the containers facing backwards, respectively, and a first or a second posture in said given direction (X B), wherein said first and second posture comprise: a) a first posture with a first side of the containers on the right of the path of advance of the containers and a second side of the containers on the left of the path of advance of the containers and a second posture with the second side of the containers on the right of the path of advance of the containers and the first side of the containers on the left of the path of advance of the containers, or b) a first posture with the first side of the containers facing upwards and the second side of the containers facing downwards and a second posture with the second side of the containers facing upwards and the first side of the containers facing downwards, the method including: - defining a desired posture for said containers in said input flow of containers, - identifying, in said input flow of containers, the containers having a posture different from said desired posture, - imparting to the containers thus identified a turnover movement around said given direction (X B; X 22) bringing them to said desired posture and obtaining a flow of containers in said given direction all having said desired posture, wherein the method includes: - distinguishing (38, 28) among said containers having said desired posture the containers with said first sense of advance and the containers with said second sense of advance, - imparting to said containers in said flow of containers all having said desired posture a rotation movement (X 36) towards said vertical position, said rotation movement (X 36) being imparted in opposed senses of rotation depending on whether the containers subjected to rotation towards said vertical position have said first or said second sense of advance in order to generate said output flow of containers, wherein the containers are in a vertical position with the same orientation. a) a first posture with a first side of the containers on the right of the path of advance of the containers and a second side of the containers on the left of the path of advance of the containers and a second posture with the second side of the containers on the right of the path of advance of the containers and the first side of the containers on the left of the path of advance of the containers, or b) a first posture with the first side of the containers facing upwards and the second side of the containers facing downwards and a second posture with the second side of the containers facing upwards and the first side of the containers facing downwards, the method including: - defining a desired posture for said containers in said input flow of containers, - identifying, in said input flow of containers, the containers having a posture different from said desired posture, - imparting to the containers thus identified a turnover movement around said given direction (X B; X 22) bringing them to said desired posture and obtaining a flow of containers in said given direction all having said desired posture, wherein the method includes: - distinguishing (38, 28) among said containers having said desired posture the containers with said first sense of advance and the containers with said second sense of advance, - imparting to said containers in said flow of containers all having said desired posture a rotation movement (X 36) towards said vertical position, said rotation movement (X 36) being imparted in opposed senses of rotation depending on whether the containers subjected to rotation towards said vertical position have said first or said second sense of advance in order to generate said output flow of containers, wherein the containers are in a vertical position with the same orientation. - defining a desired posture for said containers in said input flow of containers, - identifying, in said input flow of containers, the containers having a posture different from said desired posture, - imparting to the containers thus identified a turnover movement around said given direction (X B; X 22) bringing them to said desired posture and obtaining a flow of containers in said given direction all having said desired posture, - distinguishing (38, 28) among said containers having said desired posture the containers with said first sense of advance and the containers with said second sense of advance, - imparting to said containers in said flow of containers all having said desired posture a rotation movement (X 36) towards said vertical position, said rotation movement (X 36) being imparted in opposed senses of rotation depending on whether the containers subjected to rotation towards said vertical position have said first or said second sense of advance in order to generate said output flow of containers, wherein the containers are in a vertical position with the same orientation.