The main goal of this work is to further investigate the classification of emission-line galaxies from the "Spectrophotometric Catalogue of H II galaxies" by Terlevich et al. (1991) in a homogeneous and objective way, using the three line-ratio diagrams, called diagnostic diagrams, of Veilleux & Osterbrock (1987). On the basis of the resulting catalogue, we critically discuss the classification methods in the optical range. In particular we compare our classification scheme to the one done by Rola et al. (1997) which is efficient for the classification of redshifted galaxies. We also propose a new diagnostic diagram involving the known intensity ratio R-23=([O II] lambda 3727+[O III] lambda 4959+[O III] lambda 5007)/H beta which appears to be a very good criterion allowing to discriminate the Seyfert 2 from H II galaxies. The revised catalogue including 314 narrow-emission-line galaxies(1) contains H II galaxies, Seyfert 2 galaxies, Low Ionization Nuclear Emission-Line Regions (hereafter LINERs) galaxies and some particular types of galaxies with the most intriguing ones, called "ambiguous", due to the ambiguity of their location in the diagnostic diagrams. These galaxies appear as H II galaxies and as active galactic nuclei (hereafter AGNs) in different diagrams of Veilleux & Osterbrock and constitute certainly a sample of particularly interesting candidates for a thorough study of connections between starbursts and AGNs.