In this paper, a semi-implicit Euler approximation scheme is proposed for a second-order homogeneous differentiator. Compared to an explicit Euler approximation, it is well-known that implicit Euler approximation scheme offers better performances like reducing high frequency oscillations. However, the implicit Euler approximation scheme works well only when dealing with classical sliding mode differentiator. In order to keep advantages of implicit Euler approximation, when this approximation is applied in case of homogeneous differentiators, a semi-implicit Euler approximation is proposed for a second-order system. Validation on real data is conducted to highlight the well-founded of the proposed differentiation strategy.