  The system of extended objects interplaying with a black hole describes or
mimics various gravitational phenomena. In this brief paper, we report the
results of stability analysis of codimension-one Dirac-Nambu-Goto branes rest
at the equatorial plane of $d$-dimensional spherical black holes, including the
Schwarzschild and Schwarzschild-(anti-)de Sitter black holes. For the
Schwarzschild and Schwarzschild-anti-de Sitter backgrounds the stability of
branes is shown analytically by means of a deformation technique. In contrast,
for the Schwarzschild-de Sitter background we demonstrate with the help of
numerics that the brane is unstable (only) against the s-wave sector of
perturbations.
