A　new　response-spectrum　mode　superposition　method,　entirely　in　real　value　form,　is　developed　to　analyze　the　maximum　structural　response　under　earthquake　ground　motion　for　generally　damped　linear　systems　with　repeated　eigenvalues　and　defective　eigenvectors.　This　algorithm　has　clear　physical　concepts　and　is　similar　to　the　complex　complete　quadratic　combination　(CCQC)　method　previously　established.　Since　it　can　consider　the　effect　of　repeated　eigenvalues,　it　is　called　the　CCQC-R　method,　in　which　the　correlation　coefficients　of　high-order　modal　responses　are　enclosed　in　addition　to　the　correlation　coefficients　in　the　normal　CCQC　method.　As　a　result,　the　formulas　for　calculating　the　correlation　coefficients　of　high-order　modal　responses　are　deduced　in　this　study,　including　displacement,　velocity　and　velocity-displacement　correlation　coefficients.　Furthermore,　the　relationship　between　high-order　displacement　and　velocity　covariance　is　derived　to　make　the　CCQC-R　algorithm　only　relevant　to　the　high-order　displacement　response　spectrum.　Finally,　a　practical　step-by-step　integration　procedure　for　calculating　high-order　displacement　response　spectrum　is　obtained　by　changing　the　earthquake　ground　motion　input,　which　is　evaluated　by　comparing　it　to　the　theory　solution　under　the　sine-wave　input.　The　method　derived　here　is　suitable　for　generally　linear　systems　with　classical　or　non-classical　damping.