In an electromagnetic cloak based on a transformation approach, reduced sets of

material properties are generally favored due to their easier implementation in reality,

although a seemingly inevitable drawback of undesired reflection exists in such cloaks.

Here we suggest using high-order transformations to create smooth moduli at the outer

boundary of the cloak, therefore completely eliminating the detrimental scattering

within the limit of geometric optics. We apply this scheme to a non-magnetic

cylindrical cloak and demonstrate that the scattered field is reduced substantially in a

cloak with optimal quadratic transformation as compared to its linear counterpart.