  We propose a novel prescription to take off the square root of Nambu-Goto
action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or
also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our
resulting action is a modified d-dimensional Polyakov action which is gauged
and possesses a Nambu n-bracket squared potential. We first spell out how the
(p+1)-dimensional diffeomorphism is realized in the lower dimensional action.
Then we discuss a possible gauge fixing of it to a direct product of
$d$-dimensional diffeomorphism and n-dimensional volume preserving
diffeomorphism. We show that the latter naturally leads to a novel Filippov-Lie
n-algebra based gauge theory action in d-dimensions.
