The recently proposed 2-D graphical representation of DNA based on four horizontal lines involves an arbitrary assignment of the four types of bases to the lines. While each such assignment is legitimate, it is desirable to have a scheme free of such arbitrary choices among non-equivalent geometrical representations. We outline one such approach, which is based on the construction of a 12-component vector whose components are the leading eigenvalues of the L/L matrices associated with DNA. The examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of different species illustrates the utility of the approach, (C) 2003 Elsevier Science B.V. All rights reserved.