Almost all existing Hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant, and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable. To overcome this defect, in this paper, a new nonparametric polynomial identification algorithm for the Hammerstein system is proposed which extends the idea in the author’s previous work on the Hammerstein system identification to a more general and practical case, where no functional value of the system nonlinearity is known a priori. Convergence and convergence rates in both uniform and global senses are established, and simulation studies demonstrate the effectiveness and advantage of the new algorithm.