In our paper On asymptotic normality of certain linear rank statistics, Statistics & Probability Letters, Volume 145, 2019, Pages 63-73, https://doi.org/10.1016/j.spl.2018.08.016., we have noticed an arithmetic error in the proof of Proposition 3.3. The latter error is easy to correct and the correction strengthens current version of Proposition 3.3. The related Proposition 3.4 remains valid without significant alterations in the proofs. Some minor typos are also fixed. (C) 2019 Elsevier B.V. All rights reserved.