ABSTRACT We conducted a high-precision elemental abundance analysis of the twin-star comoving pair HIP 34407/HIP 34426. With mean error of 0.013 dex in the differential abundances (Δ[X/H]), a significant difference was found: HIP 34407 is more metal rich than HIP 34426. The elemental abundance differences correlate strongly with condensation temperature, with the lowest for the volatile elements like carbon around 0.05 ± 0.02 dex, and the highest up to about 0.22 ± 0.01 dex for the most refractory elements like aluminium. Dissimilar chemical composition for stars in twin-star comoving pairs is not uncommon, thus we compile previously published results like ours and look for correlations between abundance differences and stellar parameters, finding no significant trends with average effective temperature, surface gravity, iron abundance, or their differences. Instead, we found a weak correlation between the absolute value of abundance difference and the projected distance between the stars in each pair that appears to be more important for elements that have a low absolute abundance. If confirmed, this correlation could be an important observational constraint for binary star system formation scenarios.