Correction to a Theorem on Total Positivity A well-known theorem states that if $f(z)$ generates a PF$_r$ sequence then $1/f(-z)$ generates a PF$_r$ sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if $f(z)$ generates a PF sequence then $1/f(-z)$ generates a PF sequence. Keywords:total positivity, Toeplitz matrix, PÃ³lya frequency sequence, skew Schur functionCategories:15A48, 15A45, 15A57, 05E05