We use the results of Hefez and Hernandez [7] to give a different proof for the classification of simple singularities of mappings
![$( \mathbb{C}^{2}, 0)$](img7.png)
with
respect to
![$\mathcal{A}$](img8.png)
equivalence done by Bruce and Gaffney [2] and give
the classification of unimodal singularities. The result are
extended to a classification over the real numbers
![$\mathbb{R}$](img9.png)
.