  We study linear nonradial perturbations and stability of a marginal stable
circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a
test particle in stationary axisymmetric spacetimes which possess a reflection
symmetry with respect to the equatorial plane. The proposed approach is applied
to Kerr solution and Majumdar-Papapetrou solution to Einstein equation.
Finally, we reexamine MSCOs for a modified metric of a rapidly spinning black
hole that has been recently proposed by Johannsen and Psaltis [PRD, 83, 124015
(2011)]. We show that, for the Johannsen and Psaltis's model, circular orbits
that are stable against radial perturbations for some parameter region become
unstable against vertical perturbations. This suggests that the last circular
orbit for this model may be larger than the ISCO.
