The present invention relates to a method for isolating pluripotent/multipotent stem cells derived from umbilical cord blood characterized by culturing monocytes isolated from umbilical cord blood in a culture vessel containing fibronectin and then harvesting stem cells from the culture the umbilical cord blood-derived pluripotent/multipotent stem cells isolated thereby and a cell therapeutic agent containing the pluripotent/multipotent stem cells derived from umbilical cord blood or cells differentiated therefrom. The present invention also relates to a novel culture media for stem cells a culture method for stem cells which is characterized by culturing and proliferating stem cells in the culture media and a method for increasing stemness of stem cells which is characterized by a sphere culture or a three-dimensional culture of stem cells.