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Bovine pericardium (BP) has been used as leaflets of prosthetic heart valves. The leaflets are sutured on metallic stents and can survive 400 million flaps (~10-year life span), unaffected by the suture holes. This flaw-insensitive fatigue resistance is unmatched by synthetic leaflets. We show that the endurance strength of BP under cyclic stretch is insensitive to cuts as long as 1 centimeter, about two orders of magnitude longer than that of a thermoplastic polyurethane (TPU). The flaw-insensitive fatigue resistance of BP results from the high strength of collagen fibers and soft matrix between them. When BP is stretched, the soft matrix enables a collagen fiber to transmit tension over a long length. The energy in the long length dissipates when the fiber breaks. We demonstrate that a BP leaflet greatly outperforms a TPU leaflet. It is hoped that these findings will aid the development of soft materials for flaw-insensitive fatigue resistance.