In the present paper, we describe LisBeth, a newly published phylogenetic program. LisBeth implements the cladistic three-item analysis for systematics and biogeography. We show how LisBeth handles character representation, character analysis, exact search functions, reconstruction of the intersection tree and other features, such as retention index, completeness index, character history and link with other programs such as PAUP*, version 4.0b10, TNT and Xper2. Using LisBeth, we reanalyze the phylogeny based on morphological characters of the order Gadiformes (Teleostei, Paracanthopterygii) published by Endo (2002) and compare our results. We also describe the generation of hypotheses of homology following Endo's guidelines versus 3ia representation schemes. We compare the topologies of all results and show the implications of the interpretation of character history.