  Let $(X,0)$ be an isolated complete intersection complex singularity ($X$ can
also be smooth at 0). Let $K$ be its link, $\cal X$ its canonical contact
structure and $\D_X$ the complex vector bundle associated to $\cal X$. We prove
that the bundle $\D_X$ is trivial if and only if the Milnor number of $X$
satisfies $\mu(X,0) \equiv (-1)^{n-1}$ modulo $(n-1)!$. This follows from a
general theorem stating that the complex orthogonal complement of a vector
field in $X$ with an isolated singularity at 0 is trivial iff the GSV-index of
$v$ is a multiple of $(n-1)!$. We have also an application to foliation theory:
a holomorphic foliation $\cal F$ in a ball $\B_r$ around the origin in $\C^3$,
with an isolated singularity at 0, admits a $C^\infty$ normal section (away
from 0) iff its multiplicity (or local index) is even, and this happens iff its
normal bundle in $\B_r \setminus \{0\}$ is topologically trivial.
