A bumper beam has a bow-formed outer profile (14), that has a central flange (16) and two webs (15, 18) and is fastened in two crash boxes (12, 13) with its central flange facing away from the crashboxes. The outer profile has a cover (15) so that the bumper beam will have a closed profile. The cover (15) has a central flange (24) and two webs (25, 26). The webs (17, 18) of the outer profile (14) are joined in pairs with the webs (25, 26) of the cover (15), and the web height of the cover at its center is bigger than the web height of the outer profile (14) at its center.