ag.algebraic geometry - Flat locus of $S_{1}$-morphism

Hi, everybody.

Consider an ${rm S}_{1}$- morphism $f:Xrightarrow S$ of reduced complex spaces. Assume that $f$ is open (universally open in Alg.geom), equidimensional with $n$-pure dimensional fiber, surjectiv. Let $U$ be the flat locus of $f$ (which is a dense open set).

Question: It is true that the codimension of $(X-U)cap X_{s}$ is of codimension 2 in the fiber $X_{s}$ ?

Remark: We can refer to the Thm 15.2.2, p.226 and Prop 4.7.10 of [EGA].

Thank you very much...

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