relative normal crossing and normal base change

Hi,

I have the following situation

$U\stackrel{i}{\rightarrow}X\stackrel{f}{\rightarrow} Y$

with $f$ a proper smooth morphism of schemes, $i:U\rightarrow X$ an open immersion such that $D=X\setminus U$ is a relative divisor with relative normal crossing over $Y$. Assume that I have a closed immersion

$S\rightarrow Y$

with $S$ a normal scheme. I know that $X^{\prime}$, the pullback of $X$ to $S$, is still smooth over $S$. Is it true that also the pullback of $D$ to $S$ is still relative normal crossing over $S$?