Method for constructing an asymmetrical reflector, comprising a first phase to construct a rear portion of the asymmetrical reflector, a second phase to construct a front portion of the asymmetrical reflector and a third phase to joint together the rear portion and the front portion of said asymmetrical reflector, the first phase to construct the rear portion of the asymmetrical reflector comprises following steps, a first step provides to construct a first rotationally symmetrical solid by rotating a first geometrical plane curve about an axis of direction, said first rotationally symmetrical solid comprises at least one focus, a second step provides to identify a vertical axis passing by said at least one focus and being perpendicular to a horizontal surface which mounts LEDs and to tilt the axis of direction by a first angle (α) with respect to the vertical axis, said first angle (α) lies on a first geometrical plane identified by the vertical axis and the axis of direction, a third step provides to cut the first rotationally symmetrical solid along a upper cutting line lying on the horizontal surface and along a lower cutting line lying on a geometrical horizontal plane being parallel to the horizontal surface adapted to create a rotationally symmetrical solid frustum comprising a hollow upper base lying on the horizontal surface and a hollow lower base lying on the geometrical horizontal plane, a fourth step provides to cut the rotationally symmetrical solid frustum along a first cutting line passing by said at least one focus lying on a geometrical cutting plane, said geometrical cutting plane being tilted by a third angle (γ) with respect to the first geometrical plane, the second phase to construct the front portion of the asymmetrical reflector comprises following steps, a first step provides to construct a second rotationally symmetrical solid by rotating a second geometrical plane curve about a geometrical axis of the second geometrical plane curve, said second rotationally symmetrical solid comprising at least two foci (201, 202), a second step provides to place a first focus of said at least two foci (201, 202) in correspondence with said at least one focus of the first rotationally symmetrical solid, a third step provides to tilt the geometrical axis by a second angle (β) on the first geometrical plane with respect to the axis of direction, a fourth step provides to cut the second rotationally symmetrical solid along the upper cutting line lying on the horizontal surface and along the lower cutting line lying on the geometrical horizontal plane adapted to create a second rotationally symmetrical solid frustum comprising a hollow upper base lying on the horizontal surface and a hollow lower base lying on the geometrical horizontal plane, a fifth step provides to cut the second rotationally symmetrical solid frustum along a second cutting line passing by said first focus and lying on a second geometrical cutting plane which is tilted by a fourth angle (δ) with respect to the geometrical cutting plane, the third phase to joint together the rear portion and the front portion of said asymmetrical reflector along the geometrical cutting plane (17, 27), wherein said hollow upper base of the rotationally symmetrical solid frustum comprising an area smaller than said hollow lower base of the rotationally symmetrical solid frustum, said geometrical horizontal plane placed at a distance from said horizontal surface, said distance measured along a vertical axis, characterized in that said distance is greater than another distance between said at least one focus and an intersection on the first geometrical plane between the vertical axis and the geometrical plane curve.