The masses of the most massive supermassive black holes (SMBHs) predicted by the MBH–σ and MBH–L relations appear to be in conflict. Which of the two relations is the more fundamental one remains an open question. NGC 1332 is an excellent example that represents the regime of conflict. It is a massive lenticular galaxy which has a bulge with a high velocity dispersion σ of ∼320 km s−1; bulge–disc decomposition suggests that only 44 per cent of the total light comes from the bulge. The MBH–σ and the MBH–L predictions for the central black hole mass of NGC 1332 differ by almost an order of magnitude. We present a stellar dynamical measurement of the SMBH mass using an axisymmetric orbit superposition method. Our SINFONI integral-field unit (IFU) observations of NGC 1332 resolve the SMBH's sphere of influence which has a diameter of ∼0.76 arcsec. The σ inside 0.2 arcsec reaches ∼400 km s−1. The IFU data allow us to increase the statistical significance of our results by modelling each of the four quadrants separately. We measure an SMBH mass of (1.45 ± 0.20) × 109 M⊙ with a bulge mass-to-light ratio of 7.08 ± 0.39 in the R band. With this mass, the SMBH of NGC 1332 is offset from the MBH–L relation by a full order of magnitude but is consistent with the MBH–σ relation.