For a positive integer \(n\) and \(t\geq 0\), a de Branges weight system is a system of nonincreasing functions \(\sigma_{m}(t)\) satisfying the differential recurrence \[ \sigma_{m}-\sigma_{m+1}= \frac{\dot{\sigma}_{m}}{m}- \frac{\dot{\sigma}_{m+1}}{m+1},\quad m=1,\dots ,n,\;\sigma_{n+1}\equiv 0. \tag{1} \] The weight system defined by the initial conditions \(\sigma_{m}(0)=n+1-m\) plays a key part in de Branges\('\) famous proof of the inequality \[ \sum_{m=1}^{n}(n+1-m)(m| c_{m}| ^{2}-4/m)\leq 0, \] for the logarithmic coefficients \(c_{m}\) of normalized univalent functions, conjectured by Milin and implying the Bieberbach conjecture. In fact, de Branges' theorem contains the inequality \[ \sum_{m=1}^{n} x_{m}(m| c_{m}| ^{2}-4/m)\leq 0, \tag{2} \] for any \(x_{m}\) that are the initial values \(\sigma_{m}(0)\) of nonincreasing weights \(\sigma_{m}\). An explicit or asymptotic knowledge of numbers \(x_{1},\dots ,x_{n}\) such that (2) holds potentially open the door to other interesting estimates. Not all of these tuples arise as initial values of the nonincreasing solutions of (1), that is via de Branges\('\) method, and their description is unknown. However, a complete description of all nonincreasing solutions of (1) is given, by the second author in 2003, in the framework of a more general setting. \textit{M.-Q. Xie}, in [''A generalization of the de Branges theorem'', Proc. Am. Math. Soc. 125, No. 12, 3605--3611 (1997; Zbl 0886.30009)], claims to obtain (2), by de Branges\('\) method, for any choice of the initial conditions satisfying \[ -x_{m}+2\sum_{k=m}^{n}(-1)^{k-m}x_{k}\geq 0,\quad m=1,\dots ,n. \tag{3} \] The purpose of this note is to explain why neither the method nor the result of Xie Ming-Qin is correct. The conclusion is as follows: if (2) is true in this case, de Branges\('\) method cannot be applied to prove it. Using a very interesting counterexample the authors show that merely under assumption (3) the inequality (2) can fail on \(S\). Precisely the result obtained by Xie Ming-Qin is false for every \(n\geq 3\).