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 thought naively  that such a statement should be contained in some classical book (*but the answers given below indicate that this might be not the case*).

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. looks like $\sum_i{\pm}x_i\frac{\partial}{\partial x_i}$).

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

**Question.** Is there a reference or short proof for the above **Statement**? Or maybe one can say that a metric satisfying Morse-Smale condition and Special Morse condition always exists?