A cornea holder for independently holding a predetermined portion of cornea tissue having a corneal button, an endothelial surface and an epithelial surface includes a one-piece, ring-like support member having a bore defining a passageway therethrough. One end of the ring-like member has a plurality of circumferentially spaced support fingers extending inwardly and upwardly therefrom. The support fingers have internally facing bevelled tips diverging outwardly from the passageway to independently support the predetermined portion of cornea tissue endothelial-side up such that the corneal button is suspended in the passageway. A cornea cutting system is also disclosed wherein a rotatable cutting element is moveable through the passageway and engageable solely with the predetermined portion of cornea tissue such that the predetermined portion of cornea tissue is cut along a circumference of the predetermined portion of cornea tissue in a manner which will preserve the number of cells in the endothelial and epithelial surfaces.