Algorithms to find new orders of skew-Hadamard matrices by complete searches are not efficient and require extensive CPU time. We consider a method relying on pre-calculation of inner product vectors aiming to reduce the search space. We apply our method to the algorithm of Seberry–Williamson to construct skew-Hadamard matrices. We find all possible solutions for ≤ 29. We use these results to improve analysis in order to reduce the search space.