Fluxonium qubit is a promising elementary building block for quantum information processing due to its long coherence time combined with a strong anharmonicity. In this paper, we realize a 60-ns direct cnot gate on two inductively coupled fluxoniums, which behave almost exactly as a pair of transversely coupled spin-1/2 systems. The cnot-gate fidelity, estimated using randomized benchmarking, was as high as 99.94%. Furthermore, the fidelity remains above 99.9% for 24 days without any recalibration between measurements. Compared with the 99.96% fidelity of a 60-ns identity gate, our data brings the investigation of the nondecoherence-related errors during logical operations down to 2×10-4. The present result adds a simple and robust two-qubit gate into the still relatively small family of the "beyond three nines"gates on superconducting qubits.