The LU-LC conjecture is an important open problem concerning the structure of entan-glement of states described in the stabilizer formalism. It states that two local unitaryequivalent stabilizer states are also local Clifford equivalent. If this conjecture were true,the local equivalence of stabilizer states would be extremely easy to characterize. Un-fortunately, however, based on the recent progress made by Gross and Van den Nest, wefind that the conjecture is false.