The invention relates to a connecting device for the connection between a brace and a formwork girder. The device incorporates respective arms (3) which terminate at one of their ends in hooks (4) which can be coupled on a first flange of the brace (1) and has flat extensions (6) extending from tubular portions (5) intended to rest on a lower projection of the formwork girder (2). It also has parallel rods (7) located with an inclination opposite to that of the arms (3) traversing the tubular portions (5), which are linked by a connecting bridge (9) traversed by a screw (10), the adjustment of which determines the movement of a clamp (11) assembled on the rods (7). The clamp is provided with locking means (12) which can be coupled to a second flange of the brace (1), opposite the first, in order to secure the connection between the brace (1) and the formwork girder (2).