The differential fault analysis of SOSEMNAUK was presented in Africacrypt in 2011. In this paper, we improve previous work with algebraic techniques which can result in a considerable reduction not only in the number of fault injections but also in time complexity. First, we propose an enhanced method to determine the fault position with a success rate up to 99% based on the single-word fault model. Then, instead of following the design of SOSEMANUK at word levels, we view SOSEMANUK at bit levels during the fault analysis and calculate most components of SOSEMANUK as bit-oriented. We show how to build algebraic equations for SOSEMANUK and how to represent the injected faults in bit-level. Finally, an SAT solver is exploited to solve the combined equations to recover the secret inner state. The results of simulations on a PC show that the full 384 bits initial inner state of SOSEMANUK can be recovered with only 15 fault injections in 3.97h.