The main goal of this work is to further investi- gate the classification of emission-line galaxies from the "Spec- trophotometric Catalogue of Hii 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 R23=((Oii)3727+(Oiii)4959+(Oiii)5007)/H which ap- pears to be a very good criterion allowing to discriminate the Seyfert 2 from Hii galaxies. The revised catalogue including 314 narrow-emission- line galaxies 1 contains Hii galaxies, Seyfert 2 galaxies, Low Ionization Nuclear Emission-Line Regions (hereafter LIN- ERs) galaxies and some particular types of galaxies with the most intriguing ones, called "ambiguous", due to the am- biguity of their location in the diagnostic diagrams. These galaxies appear as Hii galaxies and as active galactic nu- clei (hereafter AGNs) in different diagrams of Veilleux & Osterbrock and constitute certainly a sample of particularly in- teresting candidates for a thorough study of connections be- tween starbursts and AGNs.