A variation of the Density Matrix Renormalization Group (DMRG) procedure, based on a simplified version suggested by Martin-Delgado et al., is developed to compute low states energies for two crossed chains within the simple tight binding model suggested earlier by P. Anderson. For comparison, our results obtained using the new procedure are presented along with those obtained by exact diagonalization. In order to make clear the procedure, some technical aspects of the  implementation of the algorithm are given in detail.