A. S. Hedayat, J. Stufken and G. Su [J. Stat. Plann. Inference 56, 307-324 (1996)] have introduced a method of constructing an orthogonal array of strength t from an orthogonal array of strength t-1, based on difference schemes. We extend this result and construct an orthogonal array of strength t+m, m≥0, from an orthogonal array of strength t-1. We study, especially, the case of linear orthogonal arrays and their parity check matrices.