One of the key factors that limit the high-power applications for a type II superconductor is the irreversibility line Hirr(T), which reflects the very boundary of resistive dissipation in the phase diagram of magnetic field versus temperature. In cuprate family, the Y-, Bi-, Hg-, and Tl-based systems have superconducting transition temperatures exceeding the liquid nitrogen boiling temperature (~77 K). However, the toxic elements Hg and Tl in the latter two systems strongly constrain the applications. The best perspective so far is relying on the YBa2Cu3O7−δ (Tc ≈ 90 K) system, which is nontoxic and has a relatively high irreversibility magnetic field. We report the study of a nontoxic superconductor (Cu,C)Ba2Ca3Cu4O11+δ with Tc = 116 K. We found that the irreversibility magnetic field is extremely high, and it thus provides great potential for applications above the liquid nitrogen temperature.