A method was proposed to improve the singularity condition of the reduced basis method in the rapid analysis of solid structures. This method examines and deals with the response basis which corresponds to the sample points in the parameter domain, and eliminates the highly linearly dependent vectors. Subsequently, the newly obtained basis is conducted by reduced QR factorization, and Galerkin projection is then performed onto the space spanned by the column vectors of the matrix 〖WTHX〗Q. Therefore, the proposed method can enhance the computational accuracy and reliability. The numerical example has demonstrated this result.