Water icing is a natural phase change phenomenon which happens frequently in nature and industry and has negative effects on a variety of applications. Deicing is essential for iced surfaces, but even for a nanoengineered superhydrophobic surface, deicing may be incomplete with many adherent unmelted ice droplets which have potential of re-icing. Here, we focused on the droplet re-icing characteristics on a solid superhydrophobic surface, which has lacked attention in previous studies. Our results show that, the nucleation and ice crystal growth characteristics of a re-icing droplet are quite different with those of a first-time icing droplet. During re-icing, secondary nucleation due to fluid shear always first occurs on the edges of unmelted ice, accompanied by fast-growing ice crystals that can trigger heterogeneous nucleation when in contact with the solid surface. The re-icing takes place under very small supercooling (less than 0.5 o C) and the superhydrophobic surface does not play a key role, meaning that any current icephobic surfaces lose their features, which poses great challenges for anti-icing. In addition, because of the small supercooling, no recalescence phenomenon appears during re-icing and the droplet keeps transparent instead of clouding. Owing to the unmelted ice floating on the top of the droplet, the droplet shape after re-icing is also distinguishing from that after normal icing but the pointy tip formation during re-icing and normal icing shows a uniformity. These results shall deepen the understanding on the anti-icing and deicing physics.