Small black holes on branes: Is the horizon regular or singular?

We investigate the following question: Consider a small mass, with epsilon (the ratio of the Schwarzschild radius and the bulk curvature length) much smaller than 1, that is confined to the TeV brane in the Randall-Sundrum I scenario. Does it form a black hole with a regular horizon, or a naked singularity? The metric is expanded in epsilon and the asymptotic form of the metric is given by the weak field approximation (linear in the mass). In first order of epsilon we show that the iteration of the weak field solution, which includes only integer powers of the mass, leads to a solution that has a singular horizon. We find a solution with a regular horizon but its asymptotic expansion in the mass also contains half integer powers.