A general complex delayed dynamical network model with asymmetric coupling matrix isconsidered in this paper. For reducing the conservativeness of synchronization criteria, several novelsynchronization stability conditions are presented by using delay decomposition methods. Theseconditions are expressed by linear matrix inequalities(LMIs), which are easily solved by availablenumerical software. Numerical examples which are widely used to study delay-dependent synchronizationstability are given to illustrate the effectiveness of the proposed methods.