We consider a difference scheme based on quadratic non-polynomial spline function for second-order singularly perturbed boundary-value problem of the form ey’’ = p(x)y’ + q(x)y + r(x), y(a)=α0, y(b) = α1. The method is shown to have second and fourth-order convergence depending on the choice of parameters α, β involved in the method. The method is tested on an example and the results found to be in agreement with theory.