Due to complex design needs and enhanced precision requirements involved in modern engineering scenarios, second and higher order eigen-sensitivity is strongly demanded in dynamic system design, analysis and identification. A new efficient method of substructure sensitivity synthesis for the nth order of eigen-sensitivity with fixed Ritz basis was proposed. By using the technology of component mode synthesis, both number of DOF (degree-of-freedom) and cost of computation were significantly reduced. Another novelty of the present method was that the Ritz basis was fixed and not dependent on the design parameter, and the derivatives of Ritz basis with respect to the design parameter were zero. This novelty made the substructure sensitivity synthesis method simple in operation and easy in implementation．