In [7] a family of spline difference scheme is derived. The El Mistikawy and Werle scheme (EMW scheme) is a member of the family. The applying of that scheme on the problem with turning point is considered in [2]. The application of another member of the family (IEMW scheme) giving a better accuracy on turning point problems is analysed in [8]. Here we consider the solving of turning point problems using a genaralized scheme from [9]. The numerical results show a better accuracy for that scheme than for the both mentioned schemes. The theoretical result is not sharp for fixed $\varepsilon$.