Abstract: A better Lyapunov function of a class of  third-order nonlinear differential equations has been constructed by the method of the energy metric algorithm,and some sufficient conditions of globally asympotic stability of zero solution are obtained.The hard condition  that Lyapunov function shoud be  infinite has been removed,and the only requirement is that the positive orbit of the equation should be bounded.The result not only covers but also  improves some of the old results.

Key words: nonlinear differential equation, globally asymptotic stability, Lyapunov function, energy metric algorithm