The phylogenetic position of the fission yeast Schizosaccharomyces pombe in the fungal Tree of Life is still controversial. Three alternative phylogenetic positions have been proposed in the literature, namely (1) a position basal to the Hemiascomycetes and Euascomycetes, (2) a position as a sister group to the Euascomycetes with the Hemiascomycetes as a basal branch, or (3) a sister group to the Hemiascomycetes with Euascomycetes as a basal branch. Here we compared 91 clusters of orthologous proteins containing a single orthologue that are shared by 19 eukaryote genomes. The major part of these 91 orthologues supports a phylogenetic position of S. pombe as a basal lineage among the Ascomycota, thus supporting the second proposition. Interestingly, part of the orthologous proteins supported a fourth, not yet described alternative, in which S. pombe is basal to both Basidiomycota and Ascomycota. Both topologies of phylogenetic trees are well supported. We believe that both reflect correctly the phylogenetic history of the species concerned. This apparent paradox may point to a heterogeneous nuclear genome of the fungi. Importantly, this needs to be taken in consideration for a correct understanding of the fungal Tree of Life.