AbstractLocated at less than two pc away, Luhman 16 AB (WISE J104915.57‐531906.1) is the closest pair of brown dwarfs and the third closest “stellar” system to Earth. An exoplanet candidate in the Luhman 16 binary system was reported in 2017 based on a weak astrometric signature in the analysis of 12 HST epochs. An additional epoch collected in 2018 and re‐analysis of the data with more advanced methods further increased the significance level of the candidate, consistent with a Neptune‐mass exoplanet orbiting one of the Luhman 16 brown dwarf components. We report the joint analysis of these previous data together with two new astrometric HST epochs we obtained to confirm or disprove this astrometric signature. Our new analysis rules out the presence of a planet orbiting one component of the Luhman 16 AB system for masses 1.5 M♆ (Neptune masses) and periods between 400 and 5000 days. However, the presence of third bodies with masses 3 M♆ and periods between 2 and 400 days (1.1 years) cannot be excluded. Our measurements make significant improvements to the characterization of this sub‐stellar binary, including its mass‐ratio 0.8305 , individual component masses 35.40.2 MꝜ and 29.40.2 MꝜ (Jupiter masses), and parallax distance 1.9960 pc 50 AU. Comparison of the masses and luminosities of Luhman 16 AB to several evolutionary models shows persistent discrepancies in the ages of the two components, but strengthens the case that this system is a member of the 51095 Myr Oceanus Moving Group.