For a two-dimensional piecewise linear map with a riddled basin, a multifractal spectrum f(γ), which characterizes the “skeletons” of the riddled basin, is introduced. With f(γ), the uncertainty exponent is obtained by a variational principle, which enables us to introduce a concept of a “boundary” for the riddled basin. A conjecture on the relation between f(γ) and the “stable sets” of various ergodic measures, which coexist with the natural invariant measure on the chaotic attractor, is also proposed.