Abstract: Blade sharpening apparatus including two final honing wheels of substantially cylindrical geometrical configuration. The wheels are nominally five inches in length and six inches in diameter, the diameter of the exit end of the wheel being approximately 0.0015 inches greater than the entrance end. The wheel mounted on either side of a continuous blade strip rotate about parallel axes which are also parallel to the edge of the blade strip. A spiral helix is formed on the surface of each wheel such that when the wheels are intermeshed a nip running along and parallel to the blade edge is formed. The material from which the wheels are fabricated is selected to have sufficient resiliency so as to form a final facet on the blade of substantially convex geometry.