Electromagnetic cloak is a device which makes an object "invisible" for electromagnetic irradiation in a certain frequency range. Material parameters for the complementary medium-assisted external cylindrical cloak with arbitrary cross section are derived based on combining the concepts of complementary media and transformation optics. It can make the object with arbitrary shape outside the cloaking domain invisible, as long as an "antiobject" is embedded in the complementary media layer. Moreover, we find that the shape, size and the position of the "antiobject" is dependent on the contour of the cloak and the coordinate transformation. The external cloaking effect has been verified by full-wave simulation.