A vertebral stabilisation device, consisting of at least two linking elements arranged to link two separate vertebrae together, and attachment elements for attaching the ends of each linking element to the two separate vertebrae, characterised in that the length of the linking elements and the arrangement of the attachment elements are such that each linking element can extend diagonally between the two vertebrae to which it is attached, intersecting the mean sagittal plane of the vertebral column, the two linking elements intersecting substantially at said plane, and in that at least the attachment elements situated on a same side of the mean sagittal plane of the vertebral column and on separate vertebrae are not attached to each other.