  Let $\mathcal{O}$ be a closed orientable 2-orbifold of negative Euler
characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic
form $\omega$ on the deformation space $\mathcal{C}(\mathcal{O})$ of convex
projective structures on $\mathcal{O}$. We show that the deformation space
$\mathcal{C}(\mathcal{O})$ of convex projective structures on $\mathcal{O}$
admits a global Darboux coordinates system with respect to $\omega$. To this
end, we show that $\mathcal{C}(\mathcal{O})$ can be decomposed into smaller
symplectic spaces. In the course of the proof, we also study the deformation
space $\mathcal{C}(\mathcal{O})$ for an orbifold $\mathcal{O}$ with boundary
and construct the symplectic form on the deformation space of convex projective
structures on $\mathcal{O}$ with fixed boundary holonomy.
