Although the titanomagnetite–ilmenite thermo-oxybarometer has been widely used to provide information on temperature and oxygen fugacity during magmatic and metamorphic processes, the available formulations yield unsatisfactory results; for example, at high temperature and low to moderate fO2 (i.e. in conditions relevant to crystallization in basic and intermediate rocks). We present a new version of this thermo-oxybarometer based on numerical fits of a large experimental dataset comprising new results in the Fe–Ti–Al–Mg–O system and those of literature studies. Our new subsolidus experimental results at temperatures in the range 1100–1300°C under low to moderate fO2 conditions show that the addition of Mg and/or Al in the concentration ranges that are usual in Fe–Ti oxides from basic magmatic rocks can be accommodated by simple projections. We have taken advantage of this fact and performed numerical fits to generate empirical formulations. With the resulting expressions we can retrieve temperature values from X′usp and X′ilm (projected mole fractions) of titanomagnetite–ilmenitess pairs and fO2 values from X′usp and T. The present thermo-oxybarometer model is designed for assemblages of titanomagnetite and hemoilmenite (with the RJOURNAL/jpetr/04.02/00009961-200806000-00005/OV0455/v/2017-10-16T173428Z/r/image-png space group), with the usual low Al2O3, Cr2O3, MgO and MnO contents (less than about 6 wt %), which equilibrated at high temperatures (T ≥800°C) and low to moderate oxygen fugacities (–4 < ΔNNO < +2, where NNO is the nickel–nickel oxide buffer). Tests of our model by using the compositions of titanomagnetite–ilmenitess pairs in products of liquidus experiments conducted at known T–fO2 conditions (literature data and new results) show that the calculated values reproduce the experimental ones within ±70°C, and in most cases within ±50°C. The estimates of the oxygen fugacity are mostly within ±0·4 log units. This is a significant improvement compared with the previous models.