In this paper we consider the issues of chaos synchronization and chaos-based secure communication when the so-called observer matching condition is not satisfied. An auxiliary drive signal vector is introduced such that the observer matching condition is satisfied. High-gain observers are employed to estimate the auxiliary drive signals as well as their derivatives in a finite time by using the drive signals of original system. Then, a kind of reduced-order observer is constructed which can directly eliminate the influence of the non-linear part and the disturbances of the system. Based on the estimates of states as well as the estimates of the auxiliary signals and their derivatives, a kind of message information recovery method is proposed. Finally, the Rössler chaotic system is used as a simulation example to verify the effectiveness of the proposed method.