  A matching $M$ in a multigraph $G=(V,E)$ is said to be uniquely restricted if
$M$ is the only perfect matching in the subgraph of $G$ induced by $V(M)$
(i.e., the set of vertices saturated by $M$). For any fixed vertex $x_0$ in
$G$, there is a bijection from the set of spanning trees of $G$ to the set of
uniquely restricted matchings of size $|V|-1$ in $S(G)-x_0$, where $S(G)$ is
the bipartite graph obtained from $G$ by subdividing each edge in $G$. Thus the
notion "uniquely restricted matchings of a bipartite graph $H$ saturating all
vertices in a partite set $X$" can be viewed as an extension of "spanning trees
in a connected graph". Motivated by this observation, we extend the notion
"G-parking functions" of a connected multigraph to "B-parking functions"
$f:X\rightarrow \{-1,0,1,2,\cdots \}$ of a bipartite graph $H$ with a
bipartition $(X,Y)$ and find a bijection $\psi$ from the set of uniquely
restricted matchings of $H$ to the set of B-parking functions of $H$. We also
show that for any uniquely restricted matching $M$ in $H$ with $|M|=|X|$, if
$f=\psi(M)$, then $\sum_{x\in X}f(x)$ is exactly the number of elements $y\in
Y-V(M)$ which are not externally B-active with respect to $M$ in $H$, where the
new notion "externally B-active members with respect to $M$ in $H$" is an
extension of "externally active edges with respect to a spanning tree in a
connected multigraph".
