A system consists of blocks (1) provided with grooves (19, 21) as well as joining elements (23) which are situated in the grooves for positioning the blocks with respect to each other. The block (1) has two joining sides (3, 5) for joining the blocks situated above and/or below it. Starting with a rough, undressed block, a layer of the rough block is removed from both joining sides over the whole surface, so that the joining sides (3, 5) become bearing surfaces (15, 17), which form the contact surfaces with the blocks above and below them. When dressing the rough block one makes sure that the distance (18) between the bearing surfaces (15, 17) lies within narrow tolerances of a desired value. Because of this, the blocks in a course lie precisely in a horizontal plane. The grooves (19, 21) and joining elements (23) make sure that the blocks lie precisely in a vertical plane. The joining element (23) is a profiled strip made of a flexible material having a width W.sub.1 which is greater than the width W.sub.2 of the grooves.