Geometry ag.algebraica – On resolution of singularities of Gorenstein

Leave $ (X, o) $ Being a singularity of Gorenstein isolated, normal, at least. $ 3 $. Leave $ pi: widetilde {X} to X $ be the singularity resolution of $ X $. Is there a hypersurface? $ H subset X $ (defined by an equation) such that strict transformation $ widetilde {H} $ of $ H $ It is regular and has the property: there is a $ 1-1 $-correspondence between the irreducible components of the exceptional divisor of $ widetilde {X} $ and that of $ widetilde {H} $?