Strain glass (STG) in Ni-rich binary Ti-Ni possesses an R-like (rhombohedral) local strain order, but it transforms into B19' martensite under stress. It remains a puzzle why the local strain order in STG yields a different long-range strain order.Here, we systematically investigated a ternary Ti 50 Ni 44.5 Fe 5.5 STG, which exhibited the same STG features as the binary STG, and the local strain order is also an R-like one.Being different from the binary STG, under stress this ternary STG transforms into a normal R-phase rather than B19'. By considering that both systems have bi-instability with respect to both R and B19' martensites in the schematic free energy landscape, we provide a unified explanation for the different products of the stress-induced STG to martensite (STG-M) transition between Ti-Ni binary system and the present ternary system. We show that the difference stems from the competing thermodynamic stability between R-phase and B19' martensites.2