  In this article, we are interested in the problem of extending the germ of a
smooth function $\tilde{f}$ defined along the standard sphere of dimension $n$
to a function defined on the ball which has no critical points. The article
gives a necessary condition using the Morse chain complex associated to the
function $f$, restriction of $\tilde{f}$ to the sphere $\mathbb{S}^n$, which is
assumed to be a Morse function.
