A locking system for mechanical joining of floorboards constructed from a body, a rear balancing layer and an upper surface layer. A strip, which is integrally formed with the body of the floorboard and which projects from a joint plane and under an adjoining board has a locking element which engages a locking groove in the rear side of the adjoining board. The joint edge provided with the strip is modified with respect to the balancing layer, for example by means of machining of the balancing layer under the strip, in order to prevent deflection of the strip caused by changes in relative humidity. Also, a floorboard provided with such a locking system, as well as a method for making floorboards with such a locking system.