In this paper, the accuracy of the Craig-Bampton method, one of the most widely used component mode synthesis methods, is improved. Considering the higher-order effect of residual modes that are simply truncated in the Craig-Bampton method, the original finite element model can be more accurately reduced. In this formulation, unknown eigenvalues are considered as additional generalized coordinates, which can be eliminated by employing the concept of system equivalent reduction expansion process. The new component mode synthesis is named the higher-order Craig-Bampton method. The formulation of the higher-order Craig-Bampton method is presented, and its improved accuracy is demonstrated through various examples.