In this paper, we give a necessary and sufficient condition for a spread to be complete, that is, an External Characterization Theorem for a complete spread: a spread $f:X\longrightarrow Z$ is complete if and only if, whenever $j:X\longrightarrow Y$ is a dense embedding with $j(X)$ locally connected in $Y$ and $g:Y\longrightarrow Z$ is a spread such that $f=g\circ j,$ then $j$ is a homeomorphism.