For the problem: $\varepsilon y''+p(x)y=f(x)$, $y(0)=\alpha_0$, $y(0)=\alpha_1$ the spline difference scheme having the second order of uniform convergence and fourth order of classical convergence is given. The scheme is a linear combination of two exponential spline difference schemes: the scheme from [2] and the one from the family given in [6]. Both of them have a second order of classical convergence. Numerical results are presented.