A kit (1) for the articulated connection between dividing panels which comprises a first pair of male pieces (2) with a coupling protrusion (3) and a second pair of female pieces (5) with a coupling hole (6), the coupling protrusions (3) and the coupling holes (6) being configured such that the protrusions are capable of engaging into the holes when a simultaneous relative vertical movement between the first and the second pair of male and female pieces (2 and 5) is produced when they are conveniently fixed to the panels, wherein one of the first or second pair of pieces (2 or 4) is also configured with a depression (14) such that the coupling protrusion or, where appropriate, the coupling hole are arranged in the cited groove, the kit comprising an auxiliary piece (8) provided with a retaining pin (13) actuatable with a lever (9) and with an angled end (13a), fixable to the lateral wing (4 or 7) of any one of the male pieces (2), the pin remaining parallel to the lateral wing and consequently outside the panel, but such that, regulated by the lever, the angled retaining end (13a) of the pin is capable of being arranged in at least two positions: a release position (A) in which the angled retaining end does not prevent the first and the second pair of pieces (2, 5) from disengaging and a locking position (B) in which the angled retaining end (13) is located in the depression (14) and exerts mechanical stop in order to prevent the relative vertical disengaging movement of the pieces (2, 5) from being undone.