A one-way gate for allowing indoor livestock, in particular a cow, to pass in one direction, comprising: - a pivoting bracket comprising a foot; - a frame comprising a body which extends in a longitudinal direction along a longitudinal axis and which in the longitudinal direction is vertically mountable to a standard or a wall, wherein the frame further comprises a first and a second leg extending at right angles to the body, which in the direction of the longitudinal axis are mutually spaced apart for receiving with the first leg and the second leg the foot of the pivoting bracket, wherein the first leg is provided with a first hole and a second hole, and wherein the second leg is provided with at least one hole (28, 30); and - a hinge pin for pivotably mounting the pivoting bracket to the frame, wherein the hinge pin has a first mounting position where the hinge pin extends through the first hole, through the foot of the pivoting bracket, and through a hole (28, 30) of the at least one hole (28, 30) in the second leg, so that a first hinge axis defined by the hinge pin includes a first angle (β) with a vertical axis so that the pivoting bracket under the influence of gravity pivots in a first pivoting direction, said one-way gate being characterized in that the hinge pin has a second mounting position where the hinge pin extends through the second hole, through the foot of the pivoting bracket, and through a hole (28, 30) of the at least one hole (28, 30) in the second leg, so that a second hinge axis defined by the hinge pin includes a second angle (γ) with the vertical axis so that the pivoting bracket under the influence of gravity pivots in a second pivoting direction, wherein the second pivoting direction is opposite to the first pivoting direction; and that said one-way gate further comprises a stop which is mounted in one of the remaining holes (24, 26, 28 or 30) through which the hinge pin does not extend. - a pivoting bracket comprising a foot; - a frame comprising a body which extends in a longitudinal direction along a longitudinal axis and which in the longitudinal direction is vertically mountable to a standard or a wall, wherein the frame further comprises a first and a second leg extending at right angles to the body, which in the direction of the longitudinal axis are mutually spaced apart for receiving with the first leg and the second leg the foot of the pivoting bracket, wherein the first leg is provided with a first hole and a second hole, and wherein the second leg is provided with at least one hole (28, 30); and - a hinge pin for pivotably mounting the pivoting bracket to the frame, wherein the hinge pin has a first mounting position where the hinge pin extends through the first hole, through the foot of the pivoting bracket, and through a hole (28, 30) of the at least one hole (28, 30) in the second leg, so that a first hinge axis defined by the hinge pin includes a first angle (β) with a vertical axis so that the pivoting bracket under the influence of gravity pivots in a first pivoting direction, said one-way gate being characterized in that the hinge pin has a second mounting position where the hinge pin extends through the second hole, through the foot of the pivoting bracket, and through a hole (28, 30) of the at least one hole (28, 30) in the second leg, so that a second hinge axis defined by the hinge pin includes a second angle (γ) with the vertical axis so that the pivoting bracket under the influence of gravity pivots in a second pivoting direction, wherein the second pivoting direction is opposite to the first pivoting direction; and that said one-way gate further comprises a stop which is mounted in one of the remaining holes (24, 26, 28 or 30) through which the hinge pin does not extend.