Abstract: A clamping jaw for clamping workpieces attached on a clamping fixture, the height of the clamping jaw being about 3.5 millimeters, or less, without sacrificing a reliable and durable connection between the clamping element and the workpiece clamped, wherein the clamping jaw is provided with two contact surfaces and clamping surfaces facing towards the workpiece and which are in active contact with the workpiece in the clamped condition and extend at right angles to one another, one or more recesses in the clamping surface, each provided with a triangular shaped inner contour, one tip of each recess faces away from the clamping surface, one clamping element is disposed in each recess, the outer contour of the clamping element corresponding to an inner contour of the recess, and an end flank of the clamping element facing towards the workpiece having clamping pin therein, and the clamping pins project beyond the clamping surface of the clamping jaw.