  The bad locus of a base-point free linear system L on a normal complex
projective variety X is defined as the subset B(L) of X of points that are not
contained in any irreducible and reduced member of L. In this paper we provide
a geometric description of such locus in terms of the morphism defined by L. In
particular, assume that the dimension of X is at least 2, and that L is the
complete linear system associated to an ample and spanned line bundle. It is
known that in this case B(L) is empty unless X is a surface. Then we prove
that, when the latter occurs, B(L) is not empty if and only if L defines a
morphism onto a two dimensional cone, in which case B(L) is the inverse image
of the vertex of the cone.
