A recent reclassification of diatoms based on phylogenies recovered using the nuclear-encoded SSU rRNA gene contains three major classes, Coscinodiscophyceae, Mediophyceae and the Bacillariophyceae (the CMB hypothesis). We evaluated this with a sequence alignment of 1336 protist and heterokont algae SSU rRNAs, which includes 673 diatoms. Sequences were aligned to maintain structural elements conserved within this dataset. Parsimony analysis rejected the CMB hypothesis, albeit weakly. Morphological data are also incongruent with this recent CMB hypothesis of three diatom clades. We also reanalyzed a recently published dataset which purports to support the CMB hypothesis. Our reanalysis found that the original analysis had not converged on the true bipartition posterior probability distribution, and rejected the CMB hypothesis. Thus we conclude that a reclassification of the evolutionary relationships of the diatoms according to the CMB hypothesis is premature.