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We present a measurement of the Hubble constant ($H_0$) using type Ia supernova (SNe Ia) in the near-infrared (NIR) from the recently updated sample of SNe Ia in nearby galaxies with distances measured via Cepheid period-luminosity relations by the SHOES project. We collect public near-infrared photometry of up to 19 calibrator SNe Ia and further 57 SNe Ia in the Hubble flow ($z>0.01$), and directly measure their peak magnitudes in the $J$ and $H$ band by Gaussian processes and spline interpolation. Calibrator peak magnitudes together with Cepheid-based distances are used to estimate the average absolute magnitude in each band, while Hubble-flow SNe are used to constrain the zero-point intercept of the magnitude-redshift relation. Our baseline result of $H_0$ is $72.3\pm1.4$ (stat) $\pm1.4$ (syst) km s$^{-1}$ Mpc$^{-1}$ in the $J$ band and $72.3\pm1.3$ (stat) $\pm1.4$ (syst) km s$^{-1}$ Mpc$^{-1}$ in the $H$ band, where the systematic uncertainties include the standard deviation of up to 21 variations of the analysis, the 0.7\% distance scale systematic from SHOES Cepheid anchors, a photometric zeropoint systematic, and a cosmic variance systematic. Our final measurement represents a measurement with a precision of 2.8\% in both bands. The variant with the largest change in $H_0$ is when limiting the sample to SNe from CSP and CfA programmes, noteworthy because these are the best calibrated, yielding $H_0\sim75$ km s$^{-1}$ Mpc$^{-1}$ in both bands. We demonstrate stretch and reddening corrections are still useful in the NIR to standardize SN Ia NIR peak magnitudes. Based on our results, in order to improve the precision of the $H_0$ measurement with SNe Ia in the NIR in the future, we would need to increase the number of calibrator SNe Ia, be able to extend the Hubble-Lemaître diagram to higher-z, and include standardization procedures to help reducing the NIR intrinsic scatter.