A locking wedge interposed between insulating material and masonry spaced from a wall structure for biasing the insulating material against the wall structure, said locking wedge having a generally U-shaped body with a pair of spaced-apart arms joined at one end by a web, said arms defining therebetween a tapered slot increasing in width towards the distal ends of the arms, said body being uniformly tapered in thickness at the said distal ends of the arms, and a plurality of equispaced transverse notches forming a serriform pattern on one face of the body substantially along the length of the arms for receiving a longitudinal rod in said notches.