Both the medical and business communities recognize that umbilical cord blood cell transplant technology could yield remarkable medical and financial profit. Several companies offering private storage and some charity community offering public umbilical cord blood banks now exist in Taiwan, 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 on property right which has 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. The wrong 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 examined the validity of the clauses of umbilical cord blood deposit contracts according to different concepts regarding the ownership of cord blood stem cell.