Species of the PST producing planktonic marine dinoflagellate genus <i>Alexandrium</i> have been intensively scrutinised, and it is therefore surprising that new taxa can still be found. Here we report a new species, <i>Alexandrium diversaporum</i> nov. sp., isolated from spherical cysts found at two sites in Tasmania, Australia. This species differs in its morphology from all previously reported <i>Alexandrium</i> species, possessing a unique combination of morphological features: the presence of 2 size classes of thecal pores on the cell surface, a medium cell size, the size and shape of the 6", 1', 2"" and Sp plates, the lack of a ventral pore, a lack of anterior and posterior connecting pores, and a lack of chain formation. We determined the relationship of the two strains to other species of <i>Alexandrium</i> based on an alignment of concatenated SSU-ITS1, 5.8S, ITS2 and partial LSU ribosomal RNA sequences, and found <i>A. diversaporum</i> to be a sister group to <i>Alexandrium leei</i> with high support. <i>A. leei</i> shares several morphological features, including the relative size and shapes of the 6", 1', 2"" and Sp plates and the fact that some strains of <i>A. leei</i> have two size classes of thecal pores. We examined <i>A. diversaporum</i> strains for saxitoxin production and found them to be non-toxic. The species lacked sequences for the domain A4 of sxtA, as has been previously found for non-saxitoxin producing species of <i>Alexandrium</i>.