  We give a characteristic free proof of the main result of our previous paper
(math.AC/0509697) concerning toroidalization of generating sequences of
valuations in dimension two function fields. We show that when an extension of
two dimensional algebraic regular local rings $R\subset S$ satisfies the
conclusions of the Strong Monomialization theorem of Cutkosky and Piltant, the
map between generating sequences in $R$ and $S$ has a toroidal structure.
