JHK photometry in the Mauna Kea Observatories (MKO) near-infrared system is presented for 115 stars. Of these stars, 79 are United Kingdom Infrared Telescope (UKIRT) standards from Hawarden et al., and 42 are Las Campanas Observatory (LCO, or NICMOS) standards from Persson et al. The average brightness of the sample in all three bandpasses is 11.5 mag, with a range between 10 and 15. The average number of nights each star was observed is 4, and the average of the internal error of the final results is 0.011 mag. These JHK data agree with those reported by other groups to 0.02 mag, for stars in common, which is consistent with the uncertainties. The measurements are used to derive colour transformations between the MKO JHK photometric system and the UKIRT, LCO and Two Micron All-Sky Survey (2MASS) systems. The 2MASS–MKO data scatter by 0.05 mag for redder stars, which is consistent with a dependence on stellar luminosity: the 2MASS J bandpass includes H2O features in dwarfs and the MKO K bandpass includes CO features in giants. We stress that colour transformations derived for stars whose spectra contain only weak features cannot give accurate transformations for objects with strong absorption features within one, but not both, of the filter bandpasses. We find evidence of systematic effects at the 0.02 mag level in the photometry of stars with J < 11 and H, K < 10.5 presented here and in Hawarden et al. This is due to an underestimate of the linearity correction for stars observed with the shortest exposure times; very accurate photometry of stars approaching the saturation limits of infrared detectors which are operated in double-read mode is difficult to obtain. There are indications that four stars in the sample, GSPC S705-D, FS 116 (B216-b7), FS 144 (Ser-EC84) and FS 32 (Feige 108), may be variable. There are 84 stars in the sample presented here that have 11 < J < 15 and 10.5 < H, K < 15, are not suspected to be variable, and have magnitudes with an estimated error ≤0.027 mag; 79 of these have an error of ≤0.020 mag. These represent the first published high-accuracy JHK stellar photometry in the MKO near-infrared photometric system; we recommend these objects be employed as primary standards for that system.