  Revised version. Proper credits added.
  In this paper we study divisorial extremal neighborhoods f:Y-->X, such that X
is a cAn type three dimensional terminal singularity, and C=f(E) is a smooth
curve, where E is the f-exceptional divisor. We view a divisorial extremal
neighborhood as a one-parameter smoothing of certain surface singularities, and
based on this we give a classification of such neighborhoods.
