  This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum
describes:
  1. the failure of the algorithm in [AMR] and [Morelli1] for the strong
factorization pointed out by Kalle Karu,
  2. the statement of a refined weak factorization theorem for toroidal
birational morphisms in [AMR], in the form utilized in [AKMR] for the proof of
the weak factorization theorem for general birationla maps, avoiding the use of
the above mentioned algorithm for the strong factorization, and 3. a list of
corrections for a few other mistakes in [AMR], mostly pointed out by Laurent
Bonavero.
