Summary: Let \(\mathcal{F}\) be a germ of holomorphic foliation with an isolated singularity at \(0 \in \mathbb{C}^2\). A characteristic curve of \(\mathcal{F}\) is a continuous one-dimensional curve tending to \(0 \in \mathbb{C}^2\), tangent to \(\mathcal{F}\) and having some ``tame'' oscillating behavior, which is a kind of generalization of a separatrix. We define a notion of resolution of the set of characteristic curves of \(\mathcal{F}\) and show that this process gives another way of obtaining the resolution of singularities of the foliation.