  The idea of a companion Lagrangian associated with $p$-Branes is extended to
include the presence of U(1) fields. The Brane Lagrangians are constructed with
$F_{ij}$ represented in terms of Lagrange Brackets, which make manifest the
reparametrisation invariance of the theory; these are replaced by Poisson
Brackets in the companion Lagrangian, which is now covariant under field
redefinition. The ensuing Lagrangians possess a similar formal structure to
those in the absence of an anti-symmetric field tensor.
