We performed a search for eclipsing and dipping sources in the archive of the EXTraS project-a systematic characterization of the temporal behavior of XMM-Newton point sources. We discovered dips in the X-ray light curve of 3XMM J004232.1+411314, which has been recently associated with the hard X-ray source dominating the emission of M31. A systematic analysis of XMM-Newton observations revealed 13 dips in 40 observations (total exposure time of ~0.8Ms). Among them, four observations show two dips, separated by ~4.01hr. Dip depths and durations are variable. The dips occur only during low-luminosity states (L_0.2-12_<1x10^38^erg/s), while the source reaches L_0.2-12_~2.8x10^38^erg/s. We propose that this system is a new dipping low-mass X-ray binary in M31 seen at high inclination (60{deg}-80{deg}); the observed dipping periodicity is the orbital period of the system. A blue HST source within the Chandra error circle is the most likely optical counterpart of the accretion disk. The high luminosity of the system makes it the most luminous (not ULX) dipper known to date.