In theory, recurring tidal disruption events (TDEs) may occur when a close stellar binary encounters a supermassive black hole, if one star is captured and undergoes repeating partial TDEs, or if both stars are tidally disrupted (double TDEs). In addition, independent TDEs may be observed over decades in some special galaxies where the TDE rate is extremely high. Exploring the diversity of recurring TDEs and probing their natures with rich observational data helps us to understand these mechanisms. We report the discovery of a second optical flare that occurred in September 2021 in IRAS F01004-2237, where a first flare that occurred in 2010 had already been reported. We also present a detailed analysis of multi-band data. We aim to understand the nature of the flare and explore the possible causes of the recurring flares. We describe our analysis of the position of the flare, the multi-band light curves (LCs), the optical and ultraviolet (UV) spectra, and the X-ray LC and spectra. The position of the flare coincides with the galaxy centre with a precision of 650 pc. The flare peaks in $ days with an absolute magnitude of $ and fades in two years, roughly following $L $. It maintains a nearly constant blackbody temperature of sim 22,000 K in later stages. Its optical and UV spectra show hydrogen and helium broad emission lines with full width at half maxima of 7,000--21,000 km s$^ $ and a He II/Halpha ratio of 0.3--2.3. It shows weak X-ray emission relative to UV emission, with X-ray flares lasting for $<2-3$ weeks, during which the spectrum is soft with a power-law index of $ $. These characters are consistent with a TDE, ruling out the possibilities of a supernova or an active galactic nucleus flare. With a TDE model, we infer a peak UV luminosity of $3.3 $ erg s$^ $ and an energy budget of $4.5 $ erg. A TDE caused the flare that occurred in 2021. The two optical flares separated by $10.3 years can be interpreted as repeating partial TDEs, double TDEs, or two independent TDEs. Although no definitive conclusion can be drawn, the partial TDEs interpretation predicts a third flare around 2033, and the independent TDEs interpretation predicts a high TDE rate of $ $ yr$^ $ in F01004-2237, both of which can be tested by future observations.
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