More recently, Beik and Salkuyeh [F. P. A. Beik and D. K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations, Computers and Mathematics with Applications, 62 (2011) 4605–4613] have presented the Gl-FOM and Gl-GMRES algorithms for solving the general coupled linear matrix equations. In this paper, two new algorithms called weighted Gl-FOM (WGl-FOM) and w...