An accessible-demountable support system for kerfed-edge wall paneling and reversible clip means used therein. The system includes vertical splines or runners each having a central web portion with pairs of front and rear flanges extending outwardly in opposite directions at right angles to the web. The front pair of flanges is adapted to be engaged in kerfs in opposing edges of wall panels. One of the rear flanges is adapted to be demountably secured to wall-mounted horizontal support members by reversible resilient clip means. The configuration of the clips is such that when one portion thereof is removably but rigidly affixed to the rear flange of a vertical spline, another portion may be hooked over an upstanding flange on a horizontal support member. This enables the simultaneous movement of the spline and clips thereon to dismount the clips from the horizontal support members, or mount and adjust the clips and spline thereon, thus providing an easily accessible-demountable support system for kerfed-edge wall construction units.