This equipment (1) comprises vertebral anchoring members (2), at least one rigid bar (3) for supporting the vertebrae, parts (4) of this(these) bar(s) (3) for connection to these anchoring members (2), and at least one assembly (10) with two antagonistic hooks (15, 16) connected to each other through a linking rod (17), a first one of these hooks (15) comprising a member (11) for its connection to a supporting bar (3). According to the invention:—the second hook (16) of said assembly (10) comprises a connecting member (11) for connecting to said supporting bar (3), and—this supporting bar (3) has a length such that it extends, after assembly on said vertebral anchoring members (2), along the connecting members (11) of both hooks (15, 16) of said assembly (10), and such that it can be connected to these connecting members (11).
