A previous self-consistent field molecular orbital method, able to describe systems having a large number of unpaired electrons, n, is reviewed and improved. This method is applied to the study of paramagnetism in large (1,000 -16,000 atoms) zigzag carbon nanotubes, represented by their n values. The computational scheme is based on the Hü ckel neglect differential overlap approach. It is shown that dependence of n on the semiempirical parameters is very small, and so they can be removed from the calculation. Enhancement of the paramagnetism (increase of n), by use of a strong external magnetic field, is also studied. Finally, the dependence of the Fermi one-electron potential energies and the spin atomic densities on both the parameters and the shape of the nanotubes is analyzed.The results have been multiplied by 10 3 , for compactness. The rows run over cycles and the columns run over atoms in a cycle.