The present invention concerns a substructure for aligning a building cover structure for an insulated wall (1), wherein said wall (1) is provided with a layer of insulation material (2), which is mounted to the wall (1) by a plurality of elongated insulation mounting members (3) and cover support profiles (4), which are mounted on the mounting members (2), comprises adjustment means for adjusting the distance between the mounting members (3) and the cover support profiles (4), wherein said adjustment means comprises two or more assembly brackets (5) mounted on at least one side of the cover support profile (4), and wherein each assembly bracket (5) comprises a cover support profile receiving first end (5A) and a distal second end (5B) adapted for penetration into the insulation material (2) on one or both sides of the insulation mounting member (3) and that the bracket is provided with apertures (11, 12) between said first and second ends (5A, 5B) receiving associated fasteners for securing the assembly bracket (5) to the cover support profile (4) and the insulation mounting members (3). This allows for a large amount of adjustment of the distance between the insulation mounting members and the cover support profiles. The adjustment system of the substructure is suitable for relative large insulation material layers, such as fibrous insulation thickness of up to 400 mm or more and the substructure according to the invention does not provide any or only a few thermal bridges as no full penetration of the insulation is needed for providing the adjustment of the cover support profile.