The present invention relates to a method of isolating a mesenchymal stem cell population from the amniotic membrane of the umbilical cord, the method comprising cultivating umbilical cord tissue in a culture medium comprising DMEM (Dulbecco's modified eagle medium), F12 (Ham's F12 Medium), M171 (Medium 171) and FBS (Fetal Bovine Serum). The invention also relates to a mesenchymal stem population isolated from the amniotic membrane of the umbilical cord, wherein at least about 90 pcnt or more cells of the stem cell population express each of the following markers: CD73, CD90 and CD105 and lack expression of the following markers: CD34, CD45 and HLA-DR. The invention also relates to a pharmaceutical composition of this mesenchymal stem population.