Abstract: The Stein factorization theorem tells that every proper holomorphic map $f:X\to S$ between complex spaces can be factorized as $f=p\circ g$ where $g:X\to Z$ is holomorphic with connected fibres and $g:Z\to S$ is finite. The properness hypothesis is important in order to avoid non-Hausdorff spaces. So it is better in the non-proper case to demand that the inverse images of small neighbourhoods (instead of the fibres) are connected. With this modification, Stein factorization holds if $f$ is compactifiable. For the proof, it is straightforward to use the compactification explicitly - but if $X$ is normal one can use the (generalized) Riemann existence theorem of Grauert-Remmert instead, a procedure which allows to weaken the compactifiability condition (in the normal case).