  The one-loop effective action for a $p$ brane embedded in a $D=p+2$ Minkowski
spacetime in the static gauge is calculated. Rescaling the quantum fluctuation
by $\sqrt{-g_0}$ evaluated on the background brane leads to the one-loop
effective action expressed only in terms of infrared and ultraviolet divergent
geometric scalars. After the infrared divergences are absorbed into the quantum
fluctuation, there remains the finite number of ultraviolet divergences. This
implies that the $D=p+2$ Poincar\'{e} symmetry and the $D=p+1$ general
coordinate invariance are preserved in one-loop order.
