The block SS–Hankel method is one of the most efficient methods for solving interior generalized eigenvalue problems (GEPs) when only the eigenvalues are required. However, even if the target GEP is Hermitian, the block SS–Hankel method does not always preserve the Hermitian structure. To overcome this issue, in this paper, we propose a structure-preserving technique of the block SS–Hankel method for solving Hermitian GEPs. We also analyse the error bound of the proposed method and show that the proposed method improves the accuracy of the eigenvalues. The numerical results support the results of the analysis.