This equipment comprises an iliac rod (2), a connection assembly (3, 4) for connecting that iliac rod to a vertebral bar, an iliac anchoring member and an iliac part connecting the iliac rod to that iliac anchoring member said connecting assembly (3, 4) is independent of the iliac rod (2) and comprises two portions, namely: —a first portion (3), for connecting to said vertebral bar (50), that forms a closed conduit (10) for engagement of that portion (3) on that bar (50) and —a second portion (4), for connecting to said iliac rod (2), that forms a conduit (12) for the engagement of that second portion (4) on the iliac rod (2). According to the invention, —said first portion is formed by a first connecting part (3) and said second portion is formed by a second connecting part (4), said first and second connecting parts (3, 4) being independent of one another said first connecting part (3) comprises a portion (3a) that forms said closed conduit (10) and a threaded rod (3b) protruding from said portion (3a) said second connecting part (4) forms a passage (11) through it for the engagement of said threaded rod (3b) of the first connecting part (3), with a pivoting capacity of said second connecting part (4) relative to said first connecting part (3).
