Multielement taxonomy and shape analysis have led to substantial revisions in the taxonomic concepts of 13 Frasnian species of Palmatolepis, which previously have been based largely on visual discrimination of the Pa elements. Septimembrate apparatuses have been recognized in three species and diagnostic Pb elements are associated with the Pa elements of eight others. The multielement reconstructions thus derived provide the a priori classification that is tested by the canonical variate analysis of the outlines of the Pa elements. The outlines are digitized from a TV image and quantified by calculating mean tangent angles within a specified number of intervals between landmarks. The mean tangent angles for each interval are the variables used in the canonical variate analysis. In a series of comparisons limited to three species each, all 13 species separate into isolated clusters that are completely congruent with the a priori groups based, with two exceptions, on multielement taxonomy. Thus, shape analysis provides a rigorous separation of closely similar species that have been difficult to distinguish by visual discrimination of the Pa elements. Shape analysis is treated herein as an integral part of the systematic descriptions. Newly described species are P. bohemica, P. boogaardi, P. luscarensis, and P. muelleri. The new taxonomic concepts lead to significant revisions in the biostratigraphic ranges of a number of species of Palmatolepis involved in the zonation and graphic correlation of the Frasnian Stage.