We report quite exotic thermoelectric power S in UBe13. At 0 T, the negative S/T continues to strongly enhance down to the superconducting transition temperature with no Fermi-liquid behavior. vertical bar S/T vertical bar is dramatically suppressed and becomes rather modest with increasing field. We have also obtained precise field dependencies of (i) an anomaly in S due to an exotic Kondo effect and (ii) a field-induced anomaly in S/T associated with the anomalous upward H-c2(T). In contrast to the field-sensitive transport property, the normal-state specific heat is magnetically robust, indicating that the largeness of the 5f density of states remains in high fields. This unusual behavior in UBe13 can be explained by a considerable change in the energy derivative of the conduction-electron lifetime tau(c)(epsilon) at the Fermi level under magnetic fields.