A clip assembly for attaching a member, such as a partition or duct, to a support covered with a layer of a fireproofing material while maintaining the integrity of the fireproofing layer, or attaching wallboard to a beam or column, has a pair of clip sub-assemblies adjustably connectible together to fit different size supports. Each clip sub-assembly is provided with a plate portion defining a planar support engaging surface substantially in the form of the outline of a right triangle and arranged particularly for gripping a flange of an I-beam and the like, while end walls perpendicular to the plate portions facilitate attachment of wallboard to the clip assembly for furring, and the like. Base portions, one of which has a slot and the other a plurality of spaced openings mateable to the slot, are connected to the plate portions and permit the adjustable connection of the clip sub-assemblies to various size supports.