  Let $(l,f):(C^2,0)\rightarrow (C^2,0)$ be the germ of a holomorphic mapping
such that $l=0$ is a smooth curve which is not a branch of the singular curve
$f=0$. The direct image of the critical locus of this mapping is called the
discriminant curve. In this paper we study the pairs $(l,f)$ for which the
discriminant curve is non-degenerate in the Kouchnirenko sense.
