There is provided a new and useful system for the construction of partition walls comprising: a floor channel adapted to be secured to a building floor; a ceiling channel adapted to be connected to a building ceiling; a series of rectangular panel assemblies each including a rectangular frame having top, bottom and side edges, a pair of rectangular panels secured to opposite sides of the frame, and a pair of adjustable support members associated with the bottom side of the frame; and wherein the side edges of the frame extend beyond the top and bottom edges thereof and include longitudinal recessed channels; and, an elongated spline including first and second lateral extensions adapted to connect two adjacent panel assemblies and to extend into the ceiling channel, the spline adapted to be moved laterally from a first position wherein the spline is contained entirely within the said recessed channel of one panel assembly to a second position wherein the first and second lateral extensions extend respectively into the adjacent recessed channels of the pair of adjacent panel assemblies.