This article proposes a new approach to identification of Hammerstein systems, where a non-linearity precedes a linear dynamic system, driven by piece-wise constant inputs. The proposed approach does not require an explicit parameterisation of the non-linearity. Moreover, the non-linearity does not have to be static, but could be the one with finite memories like backlash. By exploiting input's piecewise constant property, the denominator of the linear system described by an ARX model is consistently identified from the information of the output only; next, a subspace direct equalisation method estimates the unmeasurable inner signal based on the resulted denominator estimate and output measurements. Contrary to the existing blind approaches, the numerator of the linear system is not required, which leads to a significant improvement of removing an error propagation. On the basis of the estimated inner signal, the measured input and output, the non-linearity and linear system are obtained separately. The proposed approach is validated and compared with two existing blind approaches through numerical and experimental examples.