  In the present paper we study normal transport surfaces in four-dimensional
Euclidean space $\mathbb{E}^{4}$ which are the generalization of surface
offsets in $\mathbb{E}^{3}$. We find some results of normal transport surfaces
in $\mathbb{E}^{4}$ of evolute and parallel type. Further, we give some
examples of these type of surfaces.
