The fourth-order symmetry energy Esym;4(A)of heavy nuclei is investigated based on the Skyrme energy density functional in combination with a local density approximation.Unlike some previous works,in our method,the interferences from the other energy terms are removed since it is completely isolated from the rest of energy terms.The calculated fourth-order symmetry energy Esym;4(A)ranging from 0.2 MeV to 0.4 MeV,as shown in Fig.1,is much less than the second-order one(for 208Pb,Esym;2(A)≈200 MeV),indicating the effect of the fourth-order symmetry energy is rather weak in finite nuclei.The underlying reason for the big difference is discussed.The Brueckner theory also gives a small fourth-order symmetry energy coefficient of nuclear matter,which is also different from recent conclusions with another methods.