A surgical appliance for slicing a sliver from the cornea comprises:a base comprising an annular suction chamber shaped to be pressed against the sclera of an eye;a cornea-shaping element situated above the base and having a surface turned to face it; anda cutting blade movable in a plane that is situated between the surface of the shaping element, and the base.According to the invention, the appliance has a general support to which the base is coupled by means enabling its position relative to the support to be adjusted along the axis of symmetry of the annular chamber, and to which the cutting blade is coupled by means enabling its position relative to the general support to be adjusted along a direction parallel to the axis of symmetry of the annular chamber and enabling it to be displaced perpendicularly to said axis.