  We prove that the stratification of the asymptotic set associated to a
polynomial mapping $F: \mathbb{C}^n \to \mathbb{C}^n$ defined by "la m\'ethode
des fa\c{c}ons" (arXiv:1407.5329) is a Thom-Mather stratification.
  Nous prouvons que la stratification de lensemble asymptotique dune
application polynomial mapping $F: \mathbb{C}^n \to \mathbb{C}^n$ d\'efinie par
"la m\'ethode des fa\c{c}ons" (arXiv:1407.5329) est une stratification de
Thom-Mather
