  We discuss an alternative form of the supersymmetric D-$p$-brane action which
is quadratic in derivatives of $X$ and linear in $F_{\mu \nu}$. This action
involves an auxiliary worldvolume tensor and generalises the simplification of
the Nambu-Goto action for $p$-branes using a symmetric metric. When the
worldvolume gauge field is abelian, it appears as a Lagrange multiplier, and
solving the constraint gives the dual form of the ($p+1$)-dimensional action
with a $p-2$ form gauge field instead of a vector gauge field. This is
illustrated by the example of the dual D-2-brane action, for which the known
result is recovered.
