ABSTRACT We present results of the investigations of the properties of the methanol J1 –J0 A−+ line series motivated by the recent serendipitous detection of the maser emission in the 141 – 140 A−+ line at 349 GHz in S255IR-SMA1 soon after the accretion burst. The study includes further observations of several lines of this series in S255IR with the SMA, a mini-survey of methanol lines in the 0.8-mm range towards a sample of bright 6.7-GHz methanol maser sources with the IRAM 30-m telescope, and theoretical modelling. We found that the maser component of the 141 – 140 A−+ line in S255IR decayed by more than order of magnitude in comparison with that in 2016. No clear sign of maser emission is observed in other lines of this series in the SMA observations except the 71 – 70 A−+ line where an additional bright component is detected at the velocity of the maser emission observed earlier in the 141 – 140 A−+ line. Our LVG model constrains the ranges of the physical parameters that match the observed emission intensities. No obvious maser emission in the J1 – J0 A−+ lines was detected in the mini-survey of the 6.7-GHz methanol maser sources, though one component in NGC 7538 may represent a weak maser. In general, the maser effect in the J1 – J0 A−+ lines may serve as a tracer of rather hot environments and in particular luminosity flaring events during high-mass star formation.