A fixing system designed to hold bone pieces (4, 5) together, said fixing system comprising: a fixing element (16) designed to be attached to a first bone piece (4), a plate (11) comprising a spherical hole (15), and a bearing (17) to hold the fixing element (16) in an angular position adjusted within the hole (15) of the plate (11), said plate being designed to be held in a second bone piece (5) and to thereby hold the bone pieces (4, 5) together, said bearing (17) having an outer surface designed to rotate within the hole (15) of said plate, said bearing ( 17) a hole (21) into which the fixing element (16) is inserted and can be adjusted angularly by turning the bearing (17) into the hole (15) of the plate (11), in which the diameter of the said hole decreases from a wider diameter in a plane that passes through a equatorial zone of the hole to narrower diameters in respective planes along the upper and lower surfaces of the plate, and said bearing (17) is provided with a first end part having a spherical surface, a second end part having a spherical surface, and groove means (32) therein to allow radial expansion of the bearing when the fixing element (16) is advanced within the bore (21) of the bearing (17), in which the groove means they are constructed and placed in the bearing to hold the bearing on the plate, and in which said groove means comprise a plurality of grooves (32) extending from the first end part of the bearing partially along the length of the bearing up to a position located more than half the length of the bearing, characterized in that, the grooves define lever-shaped petals (35) around said bearing, the element comprising fixing part a part with a diameter that is greater than a diameter of a part of the hole comprising the lever-shaped petals (35), such that the advance of the bone fixing element (16) towards said part inside of said bore (21) causes the tips of the lever-shaped petals (35) to move outwardly to cause the spherical surface
