The classical taxonomy of fossil invertebrates is based on subjective judgments of morphology, which can cause confusion since there are no codified standards for the classification of genera. Here, we explore the validity of the genus taxonomy of 75 species and morphospecies of the Follicucullidae, a Late Paleozoic family of radiolarians, using a new method, Hayashi’s quantification theory II (HQT-II), a general multivariate statistical method for categorical datasets relevant to discriminant analysis. We identify a scheme of ten genera rather than the currently accepted three genera (Follicucullus, Ishigaconus and Parafollicucullus). As HQT-II cannot incorporate stratigraphic data, a phylogenetic tree of Follicucullidae was reconstructed for 38 species using maximum parsimony. Six lineages emerged, roughly in concordance with the results of HQT-II. Combined with parsimony ancestral state reconstruction, the ancestral group of this family is Haplodiacanthus. Five other groups were discriminated, the Parafollicucullus, Curvalbaillella, Pseudoalbaillella, Longtanella, and Follicucullus–Cariver lineages. The morphological evolution of these lineages comprises a minimum essential list of eight states of four traits. HQT-II is a novel discriminant analytical multivariate method that may be of value in other taxonomic problems of paleobiology.