We present photometry and moderate-resolution spectroscopy of the luminous red variable [HBS2006] 40671 originally detected as a possible nova in the galaxy M33. We found that the star is a pulsating Mira-type variable with a long period of 665 days and an amplitude exceeding 7 mag in the R band. [HBS2006] 40671 is the first confirmed Mira-type star in M33. It is one of the most luminous Mira-type variables. In the K band its mean absolute magnitude is M_K = -9.5, its bolometric magnitude measured in the maximum light is also extreme, M_bol = -7.4. The spectral type of the star in the maximum is M2e - M3e. The heliocentric radial velocity of the star is -475 km/s. There is a big negative excess (-210~km/s) in radial velocity of [HBS2006] 40671 relative to the average radial velocity of stars in its neighborhood pointing at an exceptional peculiar motion of the star. All the extreme properties of the new Mira star make it important for further studies.
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