  Recently, Choi \emph{et al}. proposed an assumption on Mayers-Lo-Chau (MLC)
no-go theorem that the state of the entire quantum system is invariable to both
participants before the unveiling phase. This means that the theorem is only
applicable to static quantum bit commitment (QBC). This paper find that the
assumption is unnecessary and the MLC no-go theorem can be applied to not only
static QBC, but also non-static one. A non-static QBC protocol proposed by Choi
\emph{et al.} is briefly reviewed and analyzed to work as a supporting example.
In addition, a novel way to prove the impossibility of the two kinds of QBC is
given.
