Let $M$ be a von Neumann algebra and let $N\subseteq M$ be a unital von Neumann subalgebra with the same identity element as $M$. If $E:M\to N$ is a normal [conditional expectation](/page/Conditional%20Expectation), meaning a normal positive unital [linear map](/page/Linear%20Map) satisfying $E(n)=n$ for every $n\in N$, then $E$ is an ultraweakly continuous linear projection of norm one from $M$ onto $N$.