  In the conventional $p$-brane theory, a gauge ($p+1$)-form field
$\phi^{(p+1)}$ mediates the interaction between $p$-branes, which is gauge
invariant in the sense $\phi^{(p+1)}\to \phi^{(p+1)}+d\Lambda^{(p)}$ with
$\Lambda^{(p)}$, an arbitrary $p$-form and $d$, a boundary operator. We, on the
contrary, propose to introduce a new gauge field $\phi^{(p+2)}$ mediating the
interaction, and we have a new type of gauge transformation: $\phi^{(p+2)}\to
\phi^{(p+2)} +\delta\Lambda^{(p+3)}$, with $\delta$, a coboundary operator.
