Abstract: A spinal osteosynthesis system includes at least a pedicular screw (1) with a head (5), a lug (2), a plate (6), elements (10) for fixing the end (4) of the lug on the head (5) including a hemispherical portion (11) integral with the head (5), a hemispherical portion (12) integral with the end (4), the portions being complementary to each other, elements for mutually fixing together the hemispherical portions, and elements (20) for fixing the plate (6) on the end (7) of the lug (2) including a hemispherical part (23) integral with the plate (6), a hemispherical part (24) integral with the end (7), the parts (24) being complementary to each other (23), and elements for mutually fixing together the hemispherical parts (23, 24) when they cooperate inside each other.