Using the Dirac-Fock relativistic wave functions in the position space the shape complexity, C-LMC(s), form of the statistical complexity measure due to Lopez-Ruiz, Mancini, and Calbet and the simple two parameter complexity measure,Gamma(alpha,beta), proposed by Shiner, Davison and Landsberg for atoms H-Lr are calculated. A comparison with the non -relativistic Hartee-Fock results is carried out to ascertain the influence of the relativistic effects on complexity. Unlike the non-relativistic Hartree-Fock results, which lead to the non-increasing C-LMC(s) the Dirac-Fock calculations lead to both C-LMC(s) and Gamma(alpha,beta) clearly displaying an increasing trend in complexity as the atomic number increases. (C) 2007 Elsevier B.V. All rights reserved.