This article investigates a new ethical basis for prohibiting human cloning from the point of view of a child's rights, and examines the limitations of human cloning in special cases. My approach appeals to two new points. (1) We must distinguish between two intentions of human cloning. One is the intention to duplicate the same genotype as the donor for the purpose of duplicating the same phenotype of that person (the intention of duplication). The other intention is to make a baby who is related to the parent by blood, in which case human cloning is not a means to the genetic duplication (the intention of non-duplication). (2) A child has a special right, "the right to an open future" (J. Feinberg), which is the collection of autonomy rights that are in trust until the child grows up. We should prohibit human cloning done with the intention of duplication, because in this case cloning will violate the cloned child's right to an open future. However,it seems there is no clear ethical ground for prohibiting human cloning when it meets the following conditions, (1) when it is done for the purpose other than duplication (the intention of non-duplication), (2) when it is in accordance with the normal reproductive rights, (3) when there is enough reason to choose cloning. Human cloning for infertility treatment seems to meet these conditions. Regarding human cloning, we must reexamine the total ethical framework of reproductive medicine.