Theorem 3 in [Goubko M. Minimizing Degree-Based Topological Indices for Trees with Given Number of Pendent Vertices // MATCH Commun. Math. Comput. Chem. 2014. V. 71, No 1. P. 33-46.] claims that the second Zagreb index M2 cannot be less than 11n - 27 for a tree with n >= 8 pendent vertices. Yet, a tree exists with n = 8 vertices (the two-sided broom) violating this inequality. The reason is that the proof of Theorem 3 relays on a tacit assumption that an index-minimizing tree contains no vertices of degree 2. This assumption appears to be invalid in general. In this note we show that the inequality M2 >= 11n-27 still holds for trees with n >= 9 vertices and provide the valid proof of the (corrected) Theorem 3.