We are studying the phase behavior of a suspension of platelike colloids which has a very broad size distribution, particularly in thickness. This suspension exhibits an isotropic--nematic phase separation over a notably wide range of particle concentrations, displaying a remarkable phenomenon. In part of the coexistence region, phase separation yields a nematic upper phase in coexistence with an isotropic bottom phase. If the nematic phase is isolated and diluted, the reverse situation is observed such that the isotropic phase now becomes the upper phase. We show that these phenomena can be explained by a pronounced fractionation with respect to platelet thickness.