When a sway force acts on a cross-bracing system, one of the braces goes into a tension state while the other goes into a compression state. The tension brace helps to stiffen the compression brace through a bolted intersecting point. This paper presents an energy method for determining the improved buckling capacity of such a compression brace. The braces considered consist of equal-leg angle members that intersect orthogonally. The present problem is more difficult to solve when compared to earlier studies made on rods and tubular brace members, because angle members may buckle in a complicated flexural torsional mode rather than in a simple flexural mode.