  For an oriented surface link $F$ in $\mathbb{R}^4$, we consider a satellite
construction of a surface link, called a 2-dimensional braid over $F$, which is
in the form of a covering over $F$. We introduce the notion of an $m$-chart on
a surface diagram $\pi(F)\subset \mathbb{R}^3$ of $F$, which is a finite graph
on $\pi(F)$ satisfying certain conditions and is an extended notion of an
$m$-chart on a 2-disk presenting a surface braid. A 2-dimensional braid over
$F$ is presented by an $m$-chart on $\pi(F)$. It is known that two surface
links are equivalent if and only if their surface diagrams are related by a
finite sequence of ambient isotopies of $\mathbb{R}^3$ and local moves called
Roseman moves. We show that Roseman moves for surface diagrams with $m$-charts
can be well-defined.
