In this paper we develop a class of accurate methods based on quartic nonpolynomial spline function at midknots for the numerical solution of a fourth order two point boundary value problems associated with plate deflection theory. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. Existing second and fourth order finite difference and spline functions based methods developed at midknots become special cases of the new approach. Convergence analysis of the proposed method is discussed. Two numerical examples are included to illustrate the practical usefulness of our method.