Abstract: A composite profile member includes two metal profile bars and at least one thermally insulating, one-piece insulating bar which engages into a clamping groove of the metal profile bars. The insulating bar is fixed in the respective clamping groove by its hook-shaped groove webs which are pressed against the insulating bar, with corresponding centering means being provided at the insulating bar and in the respective clamping groove to assure dimensional accuracy when the groove webs are pressed on. The centering means in the bottom of the respective clamping groove is a centering groove which has a trapezoidal cross section that widens in the direction toward the insulating bar and the centering means in the parts of the insulating bar which engage in the clamping grooves are members which have a trapezoidal cross section that becomes narrower toward the metal profile bars so as to engage in a centering manner in the respective centering groove.