www.elsevier.com/locate/disc In this paper, by using the repeating-column difference matrices and orthogonal decompositions of projection matrices, we propose a new general approach to construct asymmetrical orthogonal arrays. As an application of the method, some new orthogonal arrays with run sizes 72 and 96 are constructed. © 2006 Elsevier B.V. All rights reserved. MSC: primary 62K15; secondary 05B