This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new sufficient condition of global asymptotic synchronization is attained from the theory of stability of time-varying systems. In addition, compared with the previously proposed method, the sufficient condition for the synchronization of two linearly coupled unified chaotic systems is simpler and le ss conservative, and the range of coupled coefficients is wider. Numerical simul ation shows the effectiveness and feasibility of this method.