A unified and self-contained approach to the block structure of Shanks' table and its cross rules is presented. Wynn's regular and Cordellier's singular cross rules are derived by the Schur complement method in a unified manner without appealing to Padé approximation. Moreover, by extending the definition of Shanks' transformation to certain biinfinite sequences and by introducing a parameter it is possible to get more consistency with respect to Moebius transformations. It is well known that Padé approximants in general don't have this property.