The present invention complete a technique of treating a corneal disorder or disease by infusion into an anterior chamber of human eyes. Specifically, the present invention based on the findings discovered that cultured human corneal endothelial cells are comprised of a plurality of subpopulations, most of them are not suitable for infusion into patients. The above-described subject was overcome by providing, as a medicament, functionally high grade quality of cells having the function of mature differentiated human corneal endothelial cells which is a specific subpopulation and characterized by their biochemical and functional phenotypes. The present invention provides such a functional mature differentiated corneal endothelial cells, medicament comprising the same, and manufacturing method, quality control and techniques related thereto.