The umbilical cord blood stem cell gains prevailing advantages over bone marrow and fetal stem cell in both technical and ethical aspect6s, which makes the business community recognize that umbilical cord blood cell transplant technology could yield significant financial profit. In Taiwan it has stimulated a ready market for blood storage, and several companies offering private storage and some charity community offering public umbilical cord blood banks now exist, which make the prevalence of umbilical cord blood stem cell storage rate estimated up to 4 per 100 births in this country. The umbilical cord stem cells, used to be regarded as delivery wastes, appear in itself legally a brand new issue both on personal rights and property rights which have never been well elaborated in the past. Disputes are certainly to arise since the umbilical cord blood stem cell so valuable a kind of substance, which urges us to pay more attention. This article elaborates mainly the ownership of the umbilical cord blood stem cells and its derivatives. The srong classic concepts are fully presented, and meanwhile this article address that mothers have the entitlement to ownership of the umbilical cord blood stem cell by all the legal, anatomical, biological, and genetic aspects. Also this article holds that the derivative inducing process of umbilical cord blood stem cell is not kind of natural breeding as coded in article 69 and 766 of Civil Code, but that of the processing work as coded in Article 784 of civil Code.