Let $X=Spec\ A$ be a normal affine variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$. Also, assume that $S\subset X$ is a prime Weil-divisor on $X$.

Now, I need to construct a birational model $g:Y\to X$ such that $Y$ and the birational transform $S'$ of $S$ are both normal and $g$ is a projective (or proper) morphism .

Since we don't have the Resolution of Singularities in characteristic $p>0$, I don't really know a good (or standard) way of doing this in higher dimension ($n>3$).

Any help will be greatly appreciated.