  Generalized pseudostandard words were introduced by de Luca and De Luca in
2006. In comparison to the palindromic and pseudopalindromic closure, only
little is known about the generalized pseudopalindromic closure and the
associated generalized pseudostandard words. We present a counterexample to
Conjecture 43 from a paper by Blondin Mass\'e et al. that estimated the
complexity of binary generalized pseudostandard words as ${\mathcal C}(n) \leq
4n$ for all sufficiently large $n$. We conjecture that ${\mathcal C}(n)<6n$ for
all $n \in \mathbb N$.
