A coauthor of mine and I want to use the following innocent looking statement in a forthcoming paper:

**Statement.** Let $M^{2n}$ be a compact manifold and let $f$ be a Morse function with critical points of even indices. Then for *some* choice of a metric $g$ on $M^{2n}$, the closure of each unstable manifold in $M^{2n}$ is a cycle of dimension equal to the index of the corresponding critical point. 

I naively thought that such a statement should follow from or be contained in some classical book, but not so certain anymore. 

Here is an idea of how to deduce the statement from the literature. Let's take the paper of Francois Laudenbach 

http://www.numdam.org/article/AST_1992__205__219_0.pdf

and look into Remark 3. This remark claims something much stronger, namely that even without assumption on even indices the union of unstable manifolds give a structure of a CW complex on $M$ *in case* there exists a metric $g$ on $M$ such that the gradient flow satisfies the Morse-Smale condition and additionally the gradient vector field is *Special Morse* (i.e. standard next to a critical point).

Unfortunately, it is not stated in this paper whether such a metric $g$ always exists.

**Question.** Is there a reference or short proof for this statement? Maybe one can say that a metric like Laudenbach wants always exists?