Abstract: Based on the study on steel angle members subject to unidirectional bending around the major axis, a global instability mode that has not been deeply explored in structural stability theory was discovered, which is called ‘non-bifurcation instability accompanied with abrupt deformation mode change’. The differences between this instability mode and the classic bifurcation instability and ultimate instability are discussed in terms of the uniqueness of the deformation routine at the critical point, as well as the triggering mechanism. It is further shown that the featured instability can be possible in other background and with other triggering mechanism, indicating that this type of instability is not limited to a specific cross-section member, a specific force mode, or a specific cause, but it has common laws. The necessity for thorough study on the potential instable behavior and mechanism, as well as the research contents, is proposed.