A novel emulsion and its preparation route were established in a quasi-ternary system with a nonionic surfactant, water, glycerol, and squalane. This emulsion is simply obtained by diluting a discontinuous cubic liquid crystal. It consists of giant floc in part, corresponding to the fraction of the discontinuous cubic liquid crystal. Contrary to common emulsification, our emulsion has an unique and abnormal shear-response: the semistable structure is breaking down gradually by applying a mechanical energy.