We prove that there is a residual subset $\mathcal{S}$ in $\text{Diff}^1(M)$
such that, for every $f\in \mathcal{S}$, any homoclinic class of $f$ with
invariant one dimensional central bundle containing saddles of different
indices (i.e. with different dimensions of the stable invariant manifold)
coincides with the support of some invariant ergodic non-hyperbolic (one of the
Lyapunov exponents is equal to zero) measure of $f$.