Let $X$ be a topological space and $$\varepsilon \ :\ 0 \to A \to B \to C \to 0$$ be an exact sequence of sheaves of ${\cal O}_X$-modules. $\varepsilon$ is said to be pure if for each point $x\in X$, the induced sequence $$0\to A_x \to B_x \to C_x \to 0$$ is pure as a sequence of ${\cal O}_{X,x}$-modules.

Is it true to say that any split exact sequence of ${\cal O}_X$-modules is pure?