A warhead or horizontal fragmentation mine, which includes an explosive charge arranged within a housing, which is covered at the front end thereof with a concave or planar coating or cladding; and a method for producing the warhead. The coating is entirely, or at least overwhelmingly, constituted of a brittle heavy-metal or hard or carbide metal with a static fracture or breaking expansion of 15 or 25%, in which the coating is decomposed during the detonation into a large number of natural fragments or splinters of certain quantity, which spread out in a definite fragment cone or fragment wedge, and wherein the ratio of the quantity of the coating to that of explosive consists of approximately 1:0.4 to 1:0.6.