We present a more efficient differential fault analysis (DFA) attack on SOSEMANUK, a new synchronous software-oriented stream cipher, which is contained in the current eSTREAM Portfolio. In the previous study, it is required around 6144 faults, 248 SOSEMANUK iterations and 238.17 bytes storage to recovers the secret inner state of the cipher. We offer an improved attack and show that only around 4608 faults, 235.16 SOSEMANUK iterations and 223.46 bytes storage are needed under the same or even weaker fault model. The simulation results of the proposed attack show that it takes about 11.35 hours when using a PC.