Phylum [Tracheophyta] Sinnott ex Caval.-Sm. (1998) - vascular plants
   Subphylum Polypodiophytina Reveal (1996) [monotypic]
     Class Polypodiopsida Cronquist, Takht. & Zimmerm. (1966) - ferns
       Subclass Polypodiidae Cronquist, Takht. & Zimmerm. (1966)
         Order Polypodiales Link (1833) - cathetogyrates
           (eupolypods)
             Suborder Aspleniineae H.Schneid. & C.J.Rothf. (2016)
               Family Blechnaceae Newman (1844) - blechnoids
                 Subfamily Blechnoideae Gasper, V. A. O. Dittrich & Salino
                   Genus Cleistoblechnum A.L. de Gasper & A. Salino in A.L. de Gasper, V.A. de O. Dittrich, A.R. Smith & A. Salino (2016)