This paper studies global instability in swing equations of multimachine power systems. Global instability is related to the undesirable phenomenon of power system, implying that most of all generators in a system coherently lose synchronism with the remaining generators of the system. By analyzing a power system with the loop transmission network, we analytically show that global instability can occur as a result of the interplay between network topology of the system and local dynamics of generators in the system. This suggests a possibility of control for global instability by varying network topology of the system.