The linear singularly perturbed boundary value problem of the second order is considered. The spline difference schemes applied on such problem give the system of the linear equations with the tridiagonal matrix of L-form. For small values of the parameter the matrix loses L-form and the system becomes unstable. At the same time the truncation error goes to infinity when small parameter goes to zero. For obtaing uniform stability and simple structure of the matrix a fitting factor of the polynomial form is introduced. Schishkin mesh is used in order to obtain uniform convergence.