Decomposition of 2-Form on 4-Dimensional Riemannian Manifold

Theorem
Let $M$ be a $4$-dimensional oriented Riemannian manifold.

Let $\omega$ be a $2$-form on $M$.

Then $\omega$ can be written uniquely as a sum of a self-dual $2$-form and an anti-self-dual $2$-form.