If $\overline{M}=A\oplus B$ what can be said about $M$'s decomposability?

Question

Let $X$ be a Banach space, and $M$ a subspace in $X$ such that $\overline{M}% =A\oplus B$, where '$\oplus $' designates the topological direct sum.

Do we have $M=A_{0}\oplus B_{0}$ such that $\overline{A_{0}}=A$ and $% \overline{B_{0}}=B$ ? Or perhaps some other property of $M$ ?

Thank you !