The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model

We present a simple and transparent analysis of custodial symmetry in the Two-Higgs-Doublet Model adopting the bilinear formalism for the Higgs potential. The method allows to derive basis-independent, necessary and sufficient conditions for the potential to be invariant under custodial transformations. The relation between the custodial transformation and UP is revisited and clarified.