In this Rapid Comunication we report a phenomenon of a one-side riddled basin where one side of the basin of attraction of an attractor on an invariant subspace (ISS) is globally riddled, while the other side is only locally riddled. This kind of basin appears due to the symmetry breaking with respect to the ISS. This one-side riddled basin can even persist beyond the blowout bifurcation, contrary to the previously reported riddled basins which exist only below the blowout transition. An experimental situation where this phenomenon can be expected is proposed.