This paper further investigates the locally and globally adaptive synchronization of united complex dynamical networks based on a new method of network split. Time-delay has been introduced into networks to split and upon which a model of united complex dynamical networks with multi-links has been constructed. Several new locally and globally asymptotically stable network synchronization criteria are deduced by using Lyapunov stability theory and some hypotheses. The validity of the results was proved through numerical simulation of this paper.