The paper concerns the study of the quadratic b-spline curve application for the regime of pre-sliding displacements in the GMS friction hysteresis model approximation. The impact of the modification on the effectiveness of modelling the friction properties and computational efficiency is analysed. The curve approximation technique with smooth quadratic b-spline, instead of piecewise linear curve generated by Maxwell elements, transforms the multi-state GMS model into a single-state model (the spline-slip model). The solution makes the precision of friction modelling in the spline-slip model independent on the number of parameters, thus eliminating the main problem of the GMS model. The simulations show that the new model incorporates all the friction modelling capabilities provided in the GMS model.