By incorporating the higher order concept, the piece-wise linear recursive convolution (PLRC) method and Crank-Nicolson Douglas-Gunn (CNDG) algorithm, the unconditionally stable complex frequency shifted nearly perfectly matched layer (CFS-NPML) is proposed to terminate the left-handed material (LHM) domain. The proposed scheme takes advantages of CFS-NPML formulation, the higher order concept PLRC method and the unconditionally stable CNDG algorithm in terms of absorb-ing performance, computational efficiency, calculation accuracy and convenient implementation. A numerical example is carried out to demonstrate the effectiveness and efficiency of the pro-posed scheme. The results indicate that the proposed scheme can not only have considerable absorbing performance but also maintain the unconditional stability of the algorithm with the en-largement of time steps.