Block ciphers are one of the most important building blocks in cryptosystems. Modern block ciphers are often iterations of several rounds and each round consists of a confusion layer and a diffusion layer. Maximum distance separable (MDS) matrices can provide maximal diffusion, but MDS matrices are not sparse and have large description resulting costly implementations in hardware and software. So it is highly nontrivial to find MDS matrices which is involutory and efficient. In this talk we study properties of block Cauchy matrices and propose generic constructions of MDS matrices based on block Cauchy matrices. Then we propose a method for the construction of d×d involutory MDS matrices. In this talk the MDS matrices are defined over the general linear groups instead of fields.