Let $C$ be a complex curve. Recall that the slope of a coherent sheaf $\mathcal{E}$ is defined by $ \mu(\mathcal{E})=\mathrm{Arg}(-\mathrm{deg}(\mathcal{E})+i\mathrm{rank}(\mathcal{E}))\in(0,\pi]. $ We say that $\mathcal{E}$ is semistable if any subsheaf $\mathcal{F}\subset \mathcal{E}$ satisfies $\mu(\mathcal{F})\le \mu(\mathcal{E})$. The Harder-Narashimhan filtration says that for any coherent sheaf $\mathcal{F}$ there is a unique filtration $ 0=\mathcal{F}_{0}\subset \mathcal{F}_{1}\subset \dots \subset \mathcal{F}_{n}=\mathcal{F} $ such that the filtration quotient $\mathcal{F}_{i}/\mathcal{F}_{i-1}$ are semistable of slope with $\mu_{i}$ with $\mu_{1}>\mu_{2}>\dots>\mu_{n}$.
Is it possible to obtain a filtration with modified condition $\mu_{1}<\mu_{2}<\dots<\mu_{n}$?